Quadratic Formula Calculator

Finds the real solutions of ax² + bx + c = 0.

1. Enter a, b, and c.
2. Read the roots, or the message that there is no real root.

Quadratic formula

Discriminant = b² − 4ac. Two real roots when it is positive: (−b ± √discriminant) / (2a). One real root when it is zero. No real root when it is negative. If a is 0 and b is not, the root of the linear equation is −c / b.

Source. For ax² + bx + c = 0 with a not zero, the discriminant is b² − 4ac. The real roots are (−b ± square root of the discriminant) / (2a) when the discriminant is not negative. A zero a reduces the equation to bx + c = 0 when b is not zero.

Updated November 1, 2026

For a = 1, b = −5, and c = 6, the equation is x² − 5x + 6 = 0. The roots are 3 and 2.

• Roots are rounded to six decimal places for display.
• If a and b are both zero, there is no equation to solve.

What does no real roots mean?

The parabola does not cross the x-axis. The solutions are complex numbers, and this page stops at the real ones.