Quadratic Equation Solver

Solve ax² + bx + c = 0 — see the discriminant, the roots and whether they are real or complex.

How to use

  1. Type the three coefficients: a (the x² term), b (the x term) and c (the constant).
  2. Read the discriminant (Δ) and the roots. Positive Δ gives two real roots, zero gives one, negative gives complex roots.
  3. The formula used is shown at the bottom. Everything runs in your browser.

About this tool

A quadratic equation is any equation of the form ax² + bx + c = 0, where a is not zero. It arises everywhere: in physics when a ball is thrown, in economics when a price curve crosses a cost curve, in engineering when a beam deflects. The solution is a formula taught in every algebra course and forgotten by most people the week after the exam — which is exactly why a solver that shows its work is useful.

This tool takes the three coefficients and computes the discriminant Δ = b² − 4ac. The sign of Δ decides everything: positive means two distinct real roots, zero means one repeated root, and negative means the roots are complex conjugates. The solver shows all three cases, including the complex roots with the imaginary part, and prints the Bhaskara formula underneath.

The calculation runs in your browser in floating-point arithmetic. For coefficients that produce very large or very small roots, rounding may show more decimal places than necessary — the tool rounds to six significant figures.

The formula

x = (−b ± √(b² − 4ac)) / 2a. Discriminant Δ = b² − 4ac.

Frequently asked questions

What if a is zero?

Then the equation is linear (bx + c = 0), not quadratic. The tool tells you so and does not solve it.

What are complex roots?

When Δ is negative, the square root produces an imaginary number. The roots are a + bi and a − bi, where i = √(−1). They are conjugates of each other.

Can I use decimals?

Yes. Type them with a dot or a comma. The tool handles both.

Is this the Bhaskara formula?

Yes. In Brazil the quadratic formula is called Bhaskara after the Indian mathematician who described a version of it in the 12th century. The formula itself was known earlier.

Does it handle cubic equations?

No. This tool solves only second-degree (quadratic) equations.

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