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Quadratic Equation

Formula

Quadratic Formula

The Quadratic Formula provides a direct method for finding the solutions of any quadratic equation written in standard form $ax^2 + bx + c = 0$ , where $a$ , $b$ , and $c$ are real numbers and $a \neq 0$ . The formula states:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

To apply the formula, identify the coefficients $a$ , $b$ , and $c$ from the equation, substitute them into the right-hand side, and then simplify the resulting expression. The $\pm$ symbol indicates that the formula generally yields two solutions — one obtained by adding the square root term and another by subtracting it. Because the Quadratic Formula is itself an equation, the result must always be written beginning with $x =$ . Repeating the formula aloud while writing it out for each problem is an effective way to commit it to memory.

Updated 2026-04-21

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