{"id":293975,"date":"2026-05-14T13:25:18","date_gmt":"2026-05-14T18:25:18","guid":{"rendered":"https:\/\/www.mometrix.com\/academy\/?page_id=293975"},"modified":"2026-08-20T11:28:48","modified_gmt":"2026-08-20T16:28:48","slug":"quadratic-calculator","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/quadratic-formula-calculator\/","title":{"rendered":"Quadratic Formula Calculator"},"content":{"rendered":"<p>Use the quadratic formula calculator below to solve quadratic equations and find the value or values of \\(x\\).<\/p>\n<div class=\"quad-calc-outer\">\n<div class=\"quad-calc-wrapper\">\n<div class=\"quad-calc-card\">\n<div class=\"quad-calc-display-wrap\">\n                <label class=\"quad-calc-display-label\" for=\"quad-calc-eq\">ENTER YOUR MATH PROBLEM HERE<\/label><input class=\"quad-calc-display\" id=\"quad-calc-eq\" type=\"text\" placeholder=\"e.g. 2x^2 + 3x - 5 = 0\" autocomplete=\"off\" spellcheck=\"false\" aria-describedby=\"quad-calc-err\">\n            <\/div>\n<div class=\"quad-calc-btn-area\">\n<div class=\"quad-calc-btn-row\">\n                    <button class=\"qcb qcb--action\" type=\"button\" onclick=\"quadCalcBack()\" aria-label=\"Backspace\">Back<\/button><br \/>\n                    <button class=\"qcb qcb--x\" type=\"button\" onclick='quadCalcAppend(\"x\")' data-tex=\"x\" aria-label=\"x\">x<\/button><br \/>\n                    <button class=\"qcb qcb--op\" type=\"button\" onclick='quadCalcAppend(\"x^2\")' data-tex=\"x^{2}\" aria-label=\"x squared\">x\u00b2<\/button><br \/>\n                    <button class=\"qcb qcb--action\" type=\"button\" onclick=\"quadCalcClear()\" aria-label=\"Clear\">AC<\/button>\n                <\/div>\n<div class=\"quad-calc-btn-row\">\n                    <button class=\"qcb qcb--op\" type=\"button\" onclick='quadCalcAppend(\"^\")' aria-label=\"Exponent\">^<\/button><br \/>\n                    <button class=\"qcb qcb--op\" type=\"button\" onclick='quadCalcAppend(\"(\")' data-tex=\"(\" aria-label=\"Open parenthesis\">(<\/button><br \/>\n                    <button class=\"qcb qcb--op\" type=\"button\" onclick='quadCalcAppend(\")\")' data-tex=\")\" aria-label=\"Close parenthesis\">)<\/button><br \/>\n                    <button class=\"qcb qcb--op\" type=\"button\" onclick='quadCalcAppend(\"=\")' data-tex=\"=\" aria-label=\"Equals\">=<\/button>\n                <\/div>\n<div class=\"quad-calc-btn-row\">\n                    <button class=\"qcb\" type=\"button\" onclick='quadCalcAppend(\"7\")'>7<\/button><br \/>\n                    <button class=\"qcb\" type=\"button\" onclick='quadCalcAppend(\"8\")'>8<\/button><br \/>\n                    <button class=\"qcb\" type=\"button\" onclick='quadCalcAppend(\"9\")'>9<\/button><br \/>\n                    <button class=\"qcb qcb--op\" type=\"button\" onclick='quadCalcAppend(\"\/\")' data-tex=\"\\div\" aria-label=\"Divide\">\u00f7<\/button>\n                <\/div>\n<div class=\"quad-calc-btn-row\">\n                    <button class=\"qcb\" type=\"button\" onclick='quadCalcAppend(\"4\")'>4<\/button><br \/>\n                    <button class=\"qcb\" type=\"button\" onclick='quadCalcAppend(\"5\")'>5<\/button><br \/>\n                    <button class=\"qcb\" type=\"button\" onclick='quadCalcAppend(\"6\")'>6<\/button><br \/>\n                    <button class=\"qcb qcb--op\" type=\"button\" onclick='quadCalcAppend(\"*\")' data-tex=\"\\times\" aria-label=\"Multiply\">\u00d7<\/button>\n                <\/div>\n<div class=\"quad-calc-btn-row\">\n                    <button class=\"qcb\" type=\"button\" onclick='quadCalcAppend(\"1\")'>1<\/button><br \/>\n                    <button class=\"qcb\" type=\"button\" onclick='quadCalcAppend(\"2\")'>2<\/button><br \/>\n                    <button class=\"qcb\" type=\"button\" onclick='quadCalcAppend(\"3\")'>3<\/button><br \/>\n                    <button class=\"qcb qcb--op\" type=\"button\" onclick='quadCalcAppend(\"-\")' data-tex=\"-\" aria-label=\"Subtract\">\u2212<\/button>\n                <\/div>\n<div class=\"quad-calc-btn-row\">\n                    <button class=\"qcb\" type=\"button\" onclick='quadCalcAppend(\"0\")'>0<\/button><br \/>\n                    <button class=\"qcb\" type=\"button\" onclick='quadCalcAppend(\".\")' aria-label=\"Decimal point\">.<\/button><br \/>\n                    <button class=\"qcb qcb--equals\" type=\"button\" onclick=\"quadCalcExecute()\" aria-label=\"Calculate\">\u23ce<\/button><br \/>\n                    <button class=\"qcb qcb--op\" type=\"button\" onclick='quadCalcAppend(\"+\")' data-tex=\"+\" aria-label=\"Add\">+<\/button>\n                <\/div>\n<\/p><\/div>\n<div class=\"quad-calc-error\" id=\"quad-calc-err\" role=\"alert\" aria-live=\"assertive\"><\/div>\n<div class=\"quad-calc-result\" id=\"quad-calc-res\" aria-live=\"polite\">\n<div class=\"quad-calc-understood\" id=\"quad-calc-understood\"><strong>We understood your equation as:<\/strong><span id=\"quad-calc-eq-rendered\"><\/span><\/div>\n<div class=\"quad-calc-steps\" id=\"quad-calc-steps\"><\/div>\n<div class=\"quad-calc-coeffs\">\n<div class=\"quad-calc-coeff-item\"><span class=\"quad-calc-coeff-label\"><span class=\"quad-tex\" data-tex=\"a\">a<\/span> (<span class=\"quad-tex\" data-tex=\"x^{2}\">x\u00b2<\/span> coefficient)<\/span><span class=\"quad-calc-coeff-value\" id=\"quad-calc-coeff-a\"><\/span><\/div>\n<div class=\"quad-calc-coeff-item\"><span class=\"quad-calc-coeff-label\"><span class=\"quad-tex\" data-tex=\"b\">b<\/span> (<span class=\"quad-tex\" data-tex=\"x\">x<\/span> coefficient)<\/span><span class=\"quad-calc-coeff-value\" id=\"quad-calc-coeff-b\"><\/span><\/div>\n<div class=\"quad-calc-coeff-item\"><span class=\"quad-calc-coeff-label\"><span class=\"quad-tex\" data-tex=\"c\">c<\/span> (constant)<\/span><span class=\"quad-calc-coeff-value\" id=\"quad-calc-coeff-c\"><\/span><\/div>\n<\/p><\/div>\n<div class=\"quad-calc-roots-label\">Solutions<\/div>\n<div class=\"quad-calc-roots\" id=\"quad-calc-roots\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p>The quadratic formula can be used to solve any quadratic equation written in standard form. The examples below show how to identify \\(a\\), \\(b\\), and \\(c\\), substitute them into the formula, and simplify the result.<\/p>\n<h2><span id=\"Quadratic_Formula_Example_1\" class=\"m-toc-anchor\"><\/span>Quadratic Formula Example 1<\/h2>\n<div style=\"border-left: solid 4px #ffcc00; border-top: solid 1px #ffcc00; border-bottom: solid 1px #ffcc00; border-right: solid 1px #ffcc00; border-radius: 0 5px 5px 0; padding: 10px; font-weight: 600; box-shadow: 1px 1px 2px grey; width: max-content; max-width: 100%; margin-bottom: 1.5em;\">\ud83d\udca1 Solve \\(x^2+5x+6=0\\)<\/div>\n<p>The quadratic formula is \\(x=\\large{\\frac{-b\\pm\\sqrt{b^2-4ac}}{2a}}\\).<\/p>\n<p>First, identify the values of \\(a\\), \\(b\\), and \\(c\\) from the equation.<\/p>\n<p style=\"text-align: center\">\\(a=1,\\: b=5,\\: c=6\\)<\/p>\n<p>Substitute these values into the quadratic formula.<\/p>\n<p style=\"text-align: center\">\\(x=\\large{\\frac{-5\\pm\\sqrt{5^2-4(1)(6)}}{2(1)}}\\)<\/p>\n<p>Simplify the expression under the square root.<\/p>\n<p style=\"text-align: center\">\\(x=\\large{\\frac{-5\\pm\\sqrt{25-24}}{2}}\\)<\/p>\n<p style=\"text-align: center\">\\(x=\\large{\\frac{-5\\pm1}{2}}\\)<\/p>\n<p>Now solve using both the plus and minus signs.<\/p>\n<p style=\"text-align: center\">\\(x=\\large{\\frac{-5+1}{2}}\\normalsize{\\:=-2}\\)<\/p>\n<p style=\"text-align: center\">\\(x=\\large{\\frac{-5-1}{2}}\\normalsize{\\:=-3}\\)<\/p>\n<p>Therefore, the solutions are \\(x=-2\\) and \\(x=-3\\).<\/p>\n<hr \/>\n<h2><span id=\"Quadratic_Formula_Example_2\" class=\"m-toc-anchor\"><\/span>Quadratic Formula Example 2<\/h2>\n<div style=\"border-left: solid 4px #ffcc00; border-top: solid 1px #ffcc00; border-bottom: solid 1px #ffcc00; border-right: solid 1px #ffcc00; border-radius: 0 5px 5px 0; padding: 10px; font-weight: 600; box-shadow: 1px 1px 2px grey; width: max-content; max-width: 100%; margin-bottom: 1.5em;\">\ud83d\udca1 Solve \\(x^2-6x+9=0\\)<\/div>\n<p>For this equation, \\(a=1,\\: b=-6,\\: c=9\\).<\/p>\n<p>Substitute these values into the quadratic formula.<\/p>\n<p style=\"text-align: center\">\\(x=\\large{\\frac{-(-6)\\pm\\sqrt{(-6)^2-4(1)(9)}}{2(1)}}\\)<\/p>\n<p>Simplify.<\/p>\n<p style=\"text-align: center\">\\(x=\\large{\\frac{6\\pm\\sqrt{36-36}}{2}}\\)<\/p>\n<p style=\"text-align: center\">\\(x=\\large{\\frac{6\\pm0}{2}}\\)<\/p>\n<p style=\"text-align: center\">\\(x=3\\)<\/p>\n<p>Because the expression under the square root equals zero, the equation has one repeated real solution.<\/p>\n<p>Therefore, \\(x=3\\).<\/p>\n<hr \/>\n<h2><span id=\"Quadratic_Formula_Example_3\" class=\"m-toc-anchor\"><\/span>Quadratic Formula Example 3<\/h2>\n<div style=\"border-left: solid 4px #ffcc00; border-top: solid 1px #ffcc00; border-bottom: solid 1px #ffcc00; border-right: solid 1px #ffcc00; border-radius: 0 5px 5px 0; padding: 10px; font-weight: 600; box-shadow: 1px 1px 2px grey; width: max-content; max-width: 100%; margin-bottom: 1.5em;\">\ud83d\udca1 Solve \\(x^2+x-1=0\\)\n<\/div>\n<p>For this equation, \\(a=1,\\: b=1,\\: c=-1\\).<\/p>\n<p>Substitute these values into the quadratic formula.<\/p>\n<p style=\"text-align: center\">\\(x=\\large{\\frac{-1\\pm\\sqrt{1^2-4(1)(-1)}}{2(1)}}\\)<\/p>\n<p>Simplify the expression under the square root.<\/p>\n<p style=\"text-align: center\">\\(x=\\large{\\frac{-1\\pm\\sqrt{1+4}}{2}}\\)<\/p>\n<p style=\"text-align: center\">\\(x=\\large{\\frac{-1\\pm\\sqrt{5}}{2}}\\)<\/p>\n<p>Since 5 has no perfect-square factors other than 1, \\(\\sqrt{5}\\) cannot be simplified further, so the exact solutions remain in radical form.<\/p>\n<p>Therefore, the solutions are \\(x=\\large{\\frac{-1+\\sqrt{5}}{2}}\\) and \\(x=\\large{\\frac{-1-\\sqrt{5}}{2}}\\).<\/p>\n<div class=\"home-buttons2\">\n<p><a href=\"https:\/\/www.mometrix.com\/academy\/using-the-quadratic-formula\/\">Learn More About the Quadratic Formula Here!<\/a><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Use the quadratic formula calculator below to solve quadratic equations and find the value or values of . 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