What is the Quadratic Equation Solver?
Solve any quadratic equation ax² + bx + c = 0 with the quadratic formula. Enter coefficients a, b, and c directly or type a full equation like x² − 5x + 6 = 0. Results include real or complex roots, the discriminant, vertex, axis of symmetry, sum and product of roots, and numbered solution steps. Free, private, and instant in your browser.
How to use the Quadratic Equation Solver
- Choose Coefficients mode or Equation mode.
- Enter a, b, c or a full quadratic equation with =.
- Set the variable letter if it is not x.
- Read roots, discriminant, vertex, and parabola direction.
- Copy the full solution for homework or notes.
Common use cases
- Finding roots of x² − 5x + 6 = 0 for algebra homework
- Checking discriminant and vertex for graphing parabolas
- Solving quadratics with complex roots like x² + 1 = 0
Frequently asked questions
- What is the quadratic formula?
- For ax² + bx + c = 0 with a ≠ 0, x = (−b ± √(b² − 4ac)) / (2a). The expression b² − 4ac is the discriminant.
- What does the discriminant tell you?
- If D > 0 there are two real roots, D = 0 gives one repeated root, and D < 0 gives two complex conjugate roots.
- What is the vertex of a parabola?
- For y = ax² + bx + c, the vertex is at x = −b/(2a). Substitute that x to find the y-coordinate.
- Can this solve linear equations?
- No — coefficient a must be non-zero. Use the general Equation Solver for linear equations.
