Quadratic Equation Solver

Quadratic Equation Solver finds every solution of ax² + bx + c = 0. It reports the discriminant and the type of solution — two real roots, one repeated root or two complex roots — handles the linear and degenerate cases when a = 0, gives exact roots where the coefficients allow and decimal roots always, and draws the parabola with its roots marked.

Quadratics appear in algebra, physics, finance and engineering. The textbook formula can silently lose accuracy for one root when b is large, so a solver that uses a numerically stable method, shows its steps and handles every special case gives answers you can rely on and learn from.

1. Enter the coefficient a of x².
2. Enter the coefficient b of x (use 0 if there is no x term).
3. Enter the constant c (use 0 if there is none).
4. Press Solve equation.
5. Read the discriminant, roots, steps and graph, then copy or download the summary.

• Two real, one repeated and complex-conjugate roots
• Linear, no-solution and infinitely-many-solution cases when a = 0
• Numerically stable root formula that keeps small roots accurate
• Exact roots as fractions or simplified square roots where possible
• Discriminant, vertex and step-by-step working
• Accurate graph of the parabola drawn from its vertex form

• Rearrange your equation into the form ax² + bx + c = 0 before entering the coefficients.
• Enter 0 for missing terms rather than leaving a box empty.
• Use the exact form for homework and the decimal form for measurements.
• Check the graph: real roots are where the curve crosses the x-axis.