Quadratic Formula Calculator
Result
Root x₁3
Root x₂2
Nature of RootsTwo distinct real roots
Discriminant (b²−4ac)1
Vertex x = −b/(2a)2.5
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Quadratic Formula Calculator — free online calculator.
Formula
x = (−b ± √(b²−4ac)) / (2a) · Discriminant = b²−4ac · Vertex: x = −b/(2a)
- Quadratic Formula Calculator calculates its result from B, A. It uses the formula x = (−b ± √(b²−4ac)) / (2a) · Discriminant = b²−4ac · Vertex: x = −b/(2a). Change any input to recalculate the result instantly.
- The main inputs are a, b, c. Enter them in the units and format shown in the calculator.
- Keep comparable quantities in compatible units whenever the formula combines or compares them.
- Changing any input above recalculates the result with the same calculation engine used by this page.
Example: Quadratic Formula
Inputs
- a: 1 x² coefficient
- b: -5 x coefficient
- c: 6 constant
Using B = 2, A = 3, the calculated result is -0.3333333333.
Sample result: Calculating…
Frequently asked questions
What does the Quadratic Formula calculate?
Quadratic Formula Calculator — free online calculator.
Which values should I enter?
Enter a, b, c using the units and format shown beside each field.
What formula does this calculator use?
The calculator uses the following relationship: x = (−b ± √(b²−4ac)) / (2a) · Discriminant = b²−4ac · Vertex: x = −b/(2a).
Why might my result differ from another source?
Results can differ when another source uses different units, rounding rules, conventions or assumptions. Compare the inputs and definitions before comparing results.
Does the result update automatically?
Yes. Changing an input updates the result using the same calculation engine shown on this page.