Math

Quadratic Equation Calculator

Find the roots of a quadratic equation of the form ax squared plus bx plus c equals zero.

This result gives the values of x where the equation equals zero, shown as two roots with their discriminant.

Formula

Roots = (−b ± square root of (b squared − 4ac)) ÷ 2a. The value b squared − 4ac is the discriminant.

How it works

Enter a, b, and c with a not zero. The calculator checks the discriminant: positive gives two real roots, zero gives one repeated root, negative gives no real roots.

Worked example

For example, with a = 1, b = -5, and c = 6, the discriminant is 25 - 24 = 1, and the roots are x = 3.0000 and x = 2.0000.

FAQs

What does the Quadratic Equation do?
It takes the values you enter and works out the quadratic equation for you, showing the result straight away.

What should I enter?
Enter ordinary numbers in the boxes above. If a value does not make sense for this calculation, the page will ask you to check it instead of showing a wrong answer.

Can I use the result for homework or everyday math?
Yes. It is a general-purpose math helper; for exam or professional work, still check the steps against your own working.

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