Quadratic Equation Solver

About this calculator

This solver finds the roots of a quadratic equation ax² + bx + c = 0 from its coefficients, using the quadratic formula, and reports the discriminant (b² − 4ac) along the way since its sign determines what kind of roots exist: positive means two distinct real roots, zero means one repeated real root, and negative means two complex roots involving the imaginary unit i, which the calculator returns rather than treating as "no solution."

Students use it to check algebra homework and to see the roots of equations that don't factor neatly by inspection, while it also comes up in physics and engineering problems that reduce to a quadratic — projectile motion, optimizing area or profit, and circuit analysis all regularly produce an ax² + bx + c = 0 that needs solving quickly and correctly, including in the complex-root case that's easy to get wrong by hand.