Quadratic Equation Solver

The Quadratic Equation Solver is a fast, reliable, and student‑friendly tool for solving equations of the form ax² + bx + c = 0. It uses the famous quadratic formula: x = [–b ± √(b² – 4ac)] / (2a). The discriminant (Δ = b² – 4ac) determines the nature of the roots. If Δ > 0, two distinct real roots appear; Δ = 0 gives one real double root; Δ < 0 yields two complex conjugate roots. Our calculator not only gives the final roots but also shows the discriminant and a step‑by‑step breakdown, making it perfect for homework, teaching, or quick checks.

Whether you’re an algebra student, engineer, or just refreshing your math skills, this solver handles any real coefficients (including fractions and decimals). The responsive layout works on mobile, tablet, and desktop. Every calculation is done with high precision using JavaScript’s native arithmetic, and complex roots are displayed in standard a+bi form. The tool is completely free, with no sign‑up or hidden ads. We’ve designed it to be as intuitive as possible: type a, b, c and hit “Solve”.

Behind the scenes, the tool checks if ‘a’ is zero (to avoid division by zero) and warns you appropriately. It also includes a handy clear button to reset inputs. The results area shows the discriminant first, followed by the simplified roots. For complex roots, we present both the real and imaginary parts neatly. All this while being SEO‑optimized and fully accessible. MultiCalculators.org aims to provide high‑quality utilities for everyday math, and this quadratic solver is one of our most used resources. Try it with any quadratic — from simple x² – 5x + 6 to tricky 2x² + 4x + 9 — and see the detailed steps.