Quadratic Formula Calculator
Solve any quadratic equation ax²+bx+c=0. Get both roots (real or complex), discriminant, vertex coordinates, and line of symmetry. Free.
Quadratic Formula Calculator
toolznova.com • Free Calculator
Solve: ax² + bx + c = 0
How to Use
Solve quadratic equations in 3 steps.
Enter Coefficient a
Enter coefficient of x² (cannot be 0).
Enter b and c
Enter coefficient of x (b) and constant term (c).
Get Solution
Click Solve for roots, discriminant, and vertex.
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Results in milliseconds.
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Mobile, tablet, desktop.
Why Solve Quadratic Equations?
- Physics: Projectile motion — time of flight and range.
- Engineering: Structural optimization and stress analysis.
- Finance: Break-even analysis with quadratic cost curves.
- Geometry: Finding dimensions from area equations.
- Algebra: Fundamental for advanced math courses.
- Computer Graphics: Ray-sphere intersection algorithms.
Tips & Examples
- Δ > 0: two distinct real roots. Δ = 0: one repeated root. Δ < 0: complex roots.
- Sum of roots = −b/a. Product of roots = c/a.
- Vertex h = −b/2a — axis of symmetry of the parabola.
- x²−5x+6=0 has roots 2 and 3 (check: (x-2)(x-3)=0).
- If a>0: parabola opens up. If a<0: opens down.
- Quadratic formula works for ALL quadratics, even non-factorable ones.
Free Quadratic Formula Calculator Online
ToolzNova's free quadratic formula calculator solves ax²+bx+c=0 for both roots (real or complex), shows discriminant type, and gives vertex coordinates and axis of symmetry.
The quadratic formula x=(-b±√(b²-4ac))/2a is guaranteed to solve any quadratic equation. The discriminant b²-4ac tells you the nature of roots before solving.
Quadratic Formula
x = (−b ± √(b²−4ac)) / 2a. Discriminant Δ = b²−4ac. Δ>0: two real roots. Δ=0: one root. Δ<0: two complex roots. Vertex: (−b/2a, c−b²/4a).