Solve ax² + bx + c = 0 with full step-by-step working, exact roots and a live graph.
A quadratic equation has the form ax² + bx + c = 0 with a ≠ 0. Its solutions come from the quadratic formula x = (−b ± √(b² − 4ac)) / 2a. The discriminant Δ = b² − 4ac decides everything: when Δ > 0 there are two real roots, when Δ = 0 there is one repeated root, and when Δ < 0 the two roots are complex conjugates. This solver shows each step, gives exact fractions and simplified radicals where possible, and plots the parabola.
The discriminant Δ = b² − 4ac tells you the number and type of solutions before you solve: positive means two distinct real roots, zero means one repeated real root, and negative means two complex roots.
Yes. You can enter values like 1/2, 0.25 or −3. The tool clears denominators to keep the arithmetic exact and still shows an accurate decimal approximation.
Leave that box empty or type 0. For example x² − 9 = 0 uses a = 1, b = 0, c = −9 and gives x = ±3.