𝑥² Math Calculator

Quadratic Formula Calculator

Solve ax² + bx + c = 0 for x using the quadratic formula and completing the square — with full working, discriminant analysis, vertex, and graph details shown step by step.

Enter Coefficients

ax² + bx + c = 0

a (coefficient of x²)

b (coefficient of x)

c (constant)

Enter coefficients a, b, c above

Formula: x = (−b ± √(b²−4ac)) / 2a

Discriminant Interpretation

Δ = b²−4ac	Nature of Roots
>0	Two distinct real roots
=0	One repeated real root
<0	Two complex (imaginary) roots

Frequently Asked Questions

What is the quadratic formula?

The quadratic formula x = (−b ± √(b²−4ac)) / 2a solves any quadratic equation ax²+bx+c=0. The ± gives two possible solutions (roots). The term b²−4ac is the discriminant.

What are complex roots?

When the discriminant is negative, the square root is imaginary. Roots take the form x = (−b ± i√|Δ|) / 2a where i=√−1. Complex roots always come in conjugate pairs.