How to Calculate Quadratic Formula: Formula, Steps & Examples
Learn how to calculate Quadratic Formula — the formula explained step by step, with worked examples and a free calculator to check your answer.
Quadratic Formula Calculator
Verified formula Updated Jun 2026 Private — runs on your device
Verified formula
Private
Root 1 (+)
2.0000
- Root 2 (−)
- 1.0000
- Discriminant (b² − 4ac)
- 1.0000
For general information only — not financial, tax, legal or medical advice. Verify before you rely on it.
How to use the Quadratic Formula Calculator
The Quadratic Formula Calculator works out your root 1 (+), along with 2 related figures in an instant. Enter a, b and c and the result updates as you type — it is free, needs no sign-up, and runs entirely in your browser so your figures stay private.
- Enter the a.
- Enter the b.
- Enter the c.
- Read off your root 1 (+), together with root 2 (−) and discriminant (b² − 4ac) — the calculator updates automatically, with no button to press.
Formula
The Quadratic Formula Calculator uses the formula:
Root 1 (+) = (-b + √(b ^ 2 - 4 × a × c)) ÷ (2 × a)
Worked example
For example, with a of 1, b of -3 and c of 2, the root 1 (+) is 2.0000.
| a | 1 |
|---|---|
| b | -3 |
| c | 2 |
| Root 1 (+) | 2.0000 |
|---|---|
| Root 2 (−) | 1.0000 |
| Discriminant (b² − 4ac) | 1.0000 |
Results are estimates for educational use, not professional advice.
Key terms explained
- Quadratic
- An equation of the form ax² + bx + c = 0, solved with the quadratic formula.
Frequently asked questions
It solves ax² + bx + c = 0 with x = (−b ± √(b² − 4ac)) ÷ 2a. For x² − 3x + 2 = 0 the roots are 2 and 1.
The discriminant b² − 4ac shows the number of real roots: positive gives two, zero gives one repeated, and negative gives no real roots.
The roots are complex, not real, so this calculator's real-root outputs will not apply. Choose coefficients that give a non-negative discriminant for real answers.
The coefficient a cannot be zero, otherwise the equation is linear, not quadratic, and the formula divides by zero.
Enter the a. Enter the b. Enter the c. Read off your root 1 (+), together with root 2 (−) and discriminant (b² − 4ac) — the calculator updates automatically, with no button to press.