What is the quadratic formula?

x = (−b ± √(b² − 4ac)) / (2a). The discriminant Δ = b² − 4ac determines whether the roots are real (Δ > 0), repeated (Δ = 0) or complex (Δ < 0).

If a = 0 the equation is no longer quadratic — it is linear (bx + c = 0) and has a single root x = −c/b. The tool shows a clear note.

How are complex roots shown?

When Δ < 0, the tool displays roots in the form p ± qi with both real and imaginary parts.

The vertex of the parabola y = ax² + bx + c is at (−b/2a, c − b²/4a). The axis of symmetry is the vertical line x = −b/2a.

Yes — all calculations run in your browser.

If a = 0 the equation is no longer quadratic — it is linear (bx + c = 0) and has a single root x = −c/b. The tool shows a clear note.

When Δ < 0, the tool displays roots in the form p ± qi with both real and imaginary parts.

The vertex of the parabola y = ax² + bx + c is at (−b/2a, c − b²/4a). The axis of symmetry is the vertical line x = −b/2a.

Yes — all calculations run in your browser.

Solve ax² + bx + c = 0 — real and complex roots, with discriminant.

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Watch a quick simulation of this tool in action — no file needed.

Follow these steps — everything happens instantly in your browser.

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Step 1. Enter the coefficients a, b and c of ax² + bx + c = 0.
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Step 2. The discriminant and root type (two real, one real, two complex) are shown.
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Step 3. See both roots, the vertex and the axis of symmetry update instantly.

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