Calculating your root 1 (+) is straightforward once you know the Quadratic Formula formula and what each input means. This guide explains the method in plain language, walks through a manual calculation, and gives worked examples you can follow — then you can do it instantly with the Quadratic Formula Calculator.
What is Quadratic Formula?
The Quadratic Formula calculation tells you your root 1 (+) from a few simple inputs. The figure you are solving for here is the root 1 (+).
The Quadratic Formula formula
The core formula is:
Root 1 (+) = (-b + √(b ^ 2 - 4 × a × c)) ÷ (2 × a)Here is what each input means:
- a — a number. Example: 1.
- b — a number. Example: -3.
- c — a number. Example: 2.
How to calculate it step by step
- Write down the a (for example, 1).
- Write down the b (for example, -3).
- Write down the c (for example, 2).
- Apply the formula above to get your root 1 (+).
- Double-check the result with the Quadratic Formula Calculator.
Worked examples
Example 1
| Input / Output | Value |
|---|---|
| a | 1 |
| b | -3 |
| c | 2 |
| Root 1 (+) | 2.0000 |
| Root 2 (−) | 1.0000 |
| Discriminant (b² − 4ac) | 1.0000 |
With a of 1, b of -3 and c of 2, the root 1 (+) works out to 2.0000.
Tips for an accurate result
- Keep your units consistent — mixing, say, months with years or grams with kilograms is the most common source of error.
- Round only at the very end. Rounding inputs early can shift the final answer noticeably.
- Re-run the numbers whenever an input changes, rather than estimating from an old result.
Prefer not to do the maths by hand? — the Quadratic Formula Calculator does it instantly, for free, with the formula and a worked example built in.
Related calculators
Continue exploring math calculators with these tools: Margin of Error Calculator, Sample Size Calculator, Confidence Interval Calculator, Coefficient of Variation Calculator, Regular Heptagon Area Calculator.