Quadratic Formula Calculator

The standard quadratic formula: x = (−b ± √(b² − 4ac)) ÷ 2a. The expression b² − 4ac is the discriminant, which decides whether the roots are real or complex.

If b² − 4ac is positive, there are two distinct real roots. If it is zero, there is one repeated real root. If it is negative, the roots are a complex conjugate pair of the form p ± qi, which the calculator displays.

With a = 0 the equation becomes linear (bx + c = 0), not quadratic, and the quadratic formula divides by 2a — which is undefined. Use a linear-equation solver instead, or enter a non-zero value for a.