Quadratic Formula Calculator

A quadratic equation has the form ax² + bx + c = 0 and its solutions are x = (−b ± √(b² − 4ac)) ÷ 2a. The expression under the root, b² − 4ac, is the discriminant and tells you the type of answer. For x² − 5x + 6 = 0, a = 1, b = −5 and c = 6, so the discriminant is 25 − 24 = 1 and x = (5 ± 1) ÷ 2, giving x = 3 and x = 2. A positive discriminant gives two real roots, zero gives one repeated root, and a negative one gives complex roots: x² + 2x + 5 = 0 has discriminant 4 − 20 = −16, so x = −1 ± 2i. The solutions are where the parabola crosses the x-axis.