Quadratic Equation Solver
Solve ax² + bx + c = 0 with step-by-step quadratic formula and a simple graph sketch.
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Inputs
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Roots
x = 3.0000, x = -0.5000
x = (−b ± √(b² − 4ac)) / 2a
y = ax² + bx + c
y
Step-by-step
| Step | Detail |
|---|---|
| 1 | a=2, b=-5, c=-3 |
| 2 | Δ = -5² − 4(2)(-3) = 49.0000 |
| 3 | x₁ = (−(-5) + √Δ) / (2·2) = 3.0000 |
| 4 | x₂ = (−(-5) − √Δ) / (2·2) = -0.5000 |
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How this calculator works
Solve ax² + bx + c = 0 with step-by-step quadratic formula and a simple graph sketch.
Quadratic formula
x = (−b ± √(b² − 4ac)) / 2a when a ≠ 0.
Example
2x² − 5x − 3 = 0 → x = 3 and x = −1/2.
Frequently asked questions
Complex roots?+
When the discriminant is negative, roots are complex conjugates.
Is the graph exact?+
The sketch samples y over x ∈ [−5, 5] for intuition — not a CAS plotter.