Free Online Quadratic Formula Solver

1. Enter coefficient a (the x² multiplier).
2. Enter coefficient b (the x multiplier).
3. Enter coefficient c (the constant term).
4. Read the discriminant and the two roots (real or complex).

The discriminant Δ = b² − 4ac decides what kind of roots a quadratic has. Δ > 0 gives two distinct real roots, Δ = 0 gives one repeated real root, and Δ < 0 gives a pair of complex conjugate roots of the form a ± bi.

This solver accepts a, b, and c as any real numbers including decimals and negatives. It returns the discriminant alongside the roots. Complex roots are rendered in the standard a + bi form so they can be copied straight into further calculations. When a = 0 the equation degenerates to linear bx + c = 0 and the tool handles that case; when both a and b are zero the result is either trivial (all x are solutions if c = 0) or contradictory.

Quadratics show up in projectile motion, revenue optimisation, and any problem where a function bends. Knowing the roots is often the entire point — they're where the function crosses zero.