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Math / Quadratic Formula

Quadratic Formula Calculator

Solve a quadratic equation ax² + bx + c = 0, reporting real roots or a complex conjugate pair and the discriminant. This makes the sign of the discriminant visible alongside the solutions. The discriminant is D=b²−4ac and roots are (−b ± √D)/(2a). If D is negative, √D is represented as an imaginary component. When D is zero, both solutions coincide at one repeated root; the denominator 2a also explains why a cannot be zero.

Your inputs

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Calculator settings

Your result
3, 2
Roots
Discriminant
1
Root count
two real roots

Example inputs shown. Adjust them to explore.

A familiar situation

Find where a quadratic model crosses zero when solving a school or engineering equation.

How to use this calculator

  1. Enter coefficient a, coefficient b, coefficient c.
  2. Select Calculate to see the answer and its breakdown.
  3. Keep a scenario, change an input and compare the results.

Use consistent units and check the assumptions below before applying the result.

How quadratic formula is calculated

The discriminant is D=b²−4ac and roots are (−b ± √D)/(2a). If D is negative, √D is represented as an imaginary component. When D is zero, both solutions coincide at one repeated root; the denominator 2a also explains why a cannot be zero. For x²−5x+6=0, D=1 and the roots are 2 and 3.

D=b²−4ac; x=(−b±√D)/(2a).
A worked example

For x²−5x+6=0, D=1 and the roots are 2 and 3.

Assumptions & useful context

The result depends on the values you enter and the method described above. Displayed numbers may be rounded; calculations use the unrounded values. Check that this model matches your situation before relying on it.

Frequently asked questions

May a be zero?

No. With a=0 the equation is linear, not quadratic.

What does a negative discriminant indicate?

There are no real roots; the two roots are complex conjugates.

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