Quadratic Equation Solver
Solve ax² + bx + c = 0 with full step-by-step working, discriminant, and vertex information.
ax² + bx + c = 0
must ≠ 0
Nature of Roots
Discriminant (Δ = b²−4ac)
Root x₁
Root x₂
Vertex (h, k)
Axis of Symmetry
Parabola Opens
Step-by-step working
How to use
- Enter the three coefficients a, b, and c for the equation ax² + bx + c = 0.
- The equation preview updates live as you type so you can verify your input.
- a must not be zero — otherwise the equation is linear, not quadratic.
- Click Solve to get the roots, discriminant, vertex, and axis of symmetry.
- When the discriminant is negative, the roots are complex (a ± bi format).
- Full step-by-step working using the quadratic formula is shown below the results.
About this Quadratic Solver
Use this free quadratic equation solver to solve equations in the form ax2 + bx + c = 0. It helps find roots, discriminants, and solutions for algebra and math practice. No signup is required, and the tool works on phones, tablets, and desktop browsers.