Quadratic Equation Calculator

Solve a quadratic equation from its three coefficients. Enter your own values below to see first root and check the method behind it.

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Your inputs

Change the example values to match your situation.

Your result

Let’s work it out.

Fill in your inputs and select Calculate.
Your result and breakdown will appear here.

How this calculator works

Quadratic formula: x = (−b ± √(b² − 4ac)) ÷ 2a. Negative discriminants produce complex roots.

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What is Quadratic Equation Calculator?

Quadratic Equation Calculator helps you solve a quadratic equation from its three coefficients.

The main result is first root, with a breakdown of second root and discriminant. The formula, example and assumptions below explain how to interpret it.

How to use Quadratic Equation Calculator

Use the example to get familiar with the form, then enter your own figures. Any rates in the example are illustrative. Check the field labels and units before calculating.

  1. Gather a in ax² + bx + c = 0, b and c. Use values from the same situation or reporting period.
  2. Replace the example a in ax² + bx + c = 0 with your own value, then complete the other fields. Check the displayed units.
  3. Select Calculate and read first root with its result breakdown. Change one input and calculate again to compare a second scenario. Reset restores the original example.
  • Enter a in ax² + bx + c = 0, at least -1000000. Decimals are accepted.
  • Enter b, at least -1000000. Decimals are accepted.
  • Enter c, at least -1000000. Decimals are accepted.

Quadratic Equation Calculator: a worked example

With the inputs below, the result is 3 (first root). Follow the example, then replace these illustrative values with your own.

Example inputs and output
Input or outputExample value
a in ax² + bx + c = 01
b-5
c6
First root3
Second root2
Discriminant1

Understanding the Quadratic Equation result

Read first root alongside second root and discriminant. These describe different parts of the same calculation.

Displayed results use a readable number of decimal places. When checking a result by hand, keep extra precision until the last step. To compare scenarios, change one input at a time and keep the others fixed.

  • Example Second root: 2
  • Example Discriminant: 1

Quadratic Equation Calculator: assumptions and common mistakes

A useful estimate starts with the right inputs. Check the following assumptions and limits before applying the result to your situation.

  • Check the base value, sample definition and chosen operation. Display rounding should come after the calculation.

For wider guidance, visit NIST statistical handbook. The formula and scope of this specific tool are stated on this page.

Quadratic Equation Calculator FAQs

What does Quadratic Equation Calculator calculate?

Quadratic Equation Calculator helps you solve a quadratic equation from its three coefficients. Its main output is first root.

What inputs do I need for Quadratic Equation Calculator?

You need a in ax² + bx + c = 0, b and c. Use the field labels and units to match your figures to the formula.

Which formula does Quadratic Equation Calculator use?

Quadratic formula: x = (−b ± √(b² − 4ac)) ÷ 2a. Negative discriminants produce complex roots.

What is a worked example for Quadratic Equation Calculator?

Example inputs: a in ax² + bx + c = 0: 1; b: -5; c: 6. The result is 3 (first root).

How should I enter a in ax² + bx + c = 0?

Enter a in ax² + bx + c = 0, at least -1000000. Decimals are accepted.

How do I choose b?

Enter b, at least -1000000. Decimals are accepted. The example uses -5; replace it if your circumstances differ.

How should I read first root?

Read first root alongside second root and discriminant. These describe different parts of the same calculation.

Why might my Quadratic Equation Calculator result differ from my records?

Check the base value, sample definition and chosen operation. Display rounding should come after the calculation. Differences in entered values, units or rounding can also change the comparison.

Can I compare two scenarios in Quadratic Equation Calculator?

Yes. Note your first first root, change a in ax² + bx + c = 0 or another input, and select Calculate again. Editing a field clears the old result so it is not mistaken for a new calculation.

Is Quadratic Equation Calculator free, and where are my inputs calculated?

This calculator is free to use without signing in. Its formula runs in your browser; calculator inputs are not sent to a calculation API. The inputs reset to the example values when you reset the form or start a fresh page.