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How do I solve a quadratic equation?

Short answer

Put the equation in the form ax^2 + bx + c = 0 and apply the quadratic formula, x = (-b plus or minus the square root of b^2 - 4ac) divided by 2a. The browser-based quadratic equation solver takes a, b and c and returns the roots and the discriminant instantly, with nothing uploaded.

The quadratic formula

A quadratic equation has the standard form ax^2 + bx + c = 0, where a is not zero. Its solutions are given by the quadratic formula: x equals negative b, plus or minus the square root of b^2 minus 4ac, all divided by 2a. The two plus-or-minus signs produce the two possible roots. Rearrange your equation so that one side equals zero before reading off a, b and c.

What the discriminant tells you

The part under the square root, b^2 minus 4ac, is called the discriminant. If it is positive there are two distinct real roots, if it is exactly zero there is one repeated real root, and if it is negative the roots are complex. The solver reports the discriminant alongside the roots, so you immediately know which case you are in. Everything is computed in your browser.

Step by step

  1. Open the solver. Open the quadratic equation solver in your browser.
  2. Enter a, b and c. Type the coefficients a, b and c from ax^2 + bx + c = 0.
  3. Read the roots. Read the two roots and the discriminant from the result.

Frequently asked questions

What if the discriminant is negative?

A negative discriminant means the equation has no real roots; the solver returns the two complex roots instead.

Does a have to be nonzero?

Yes. If a is zero the equation is linear, not quadratic, and the quadratic formula does not apply.

Is anything sent to a server?

No. The solver runs entirely in your browser.

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