Quadratic equation solver
Solve ax² + bx + c = 0: discriminant, roots and vertex of the parabola.
How it works
Δ = b² − 4ac. If Δ > 0: two roots (−b ± √Δ) / 2a; if Δ = 0: one root −b / 2a; if Δ < 0: complex roots.
Results are for guidance only and do not replace professional advice.
Worked example
With the default values:
- a1
- b-3
- c2
you get:
- Rootsx₁ = 1 x₂ = 2
- Discriminant Δ1
- Vertex(1.5 ; -0.25)
Frequently asked questions
How does the “Quadratic equation solver” tool work?
Δ = b² − 4ac. If Δ > 0: two roots (−b ± √Δ) / 2a; if Δ = 0: one root −b / 2a; if Δ < 0: complex roots.
What do I need to enter?
Just fill in: a, b, c. The result updates as you type.
Can you give an example?
a: 1; b: -3; c: 2 → Roots: x₁ = 1 x₂ = 2; Discriminant Δ: 1.
Is this calculator free, and is my data private?
Yes. HOD Calc is completely free with no sign-up. The calculation runs in your browser: nothing you type is sent or stored.