Worked example: Quadratic Formula Calculator
Roots 1 and 2. This fixed reference example shows one complete scenario; the interactive results above use your current inputs.
View the example inputs
- Coefficient a
- 1
- Coefficient b
- -3
- Coefficient c
- 2
| Calculated quantity | Example result |
|---|---|
| Discriminant of normalized coefficients | 0.1111 |
| First root | 2 |
| Second root | 1 |
Understanding an equation’s operations and domain
Write the intended operation explicitly
Parentheses establish how a compound expression is grouped. Exponentiation, a unary minus and multiplication need not have the same precedence. The expression tool documents its supported operators and functions, and scientific calculations require the correct angle convention.
The real-number domain matters. A zero denominator, a logarithm of a nonpositive number or an even root of a negative radicand can make an otherwise familiar formula undefined in real arithmetic. Some tools explicitly return complex roots; others reject non-real results.
Check a result against the original question
A correct numeric operation can still answer the wrong question if the inputs represent different quantities. Confirm whether you are finding a percent of a base, a ratio, a distance, a root or a solution of an equation.
The worked example below makes the variables and expected output concrete. Floating-point arithmetic can round non-integer quantities; tools that use exact fractions or large integers identify that separate method.
Formula and calculation method
D=b²−4ac; x=(−b±sqrt(D))/(2a). Coefficients are divided by their largest absolute value before computing the displayed normalized discriminant. Distinct real roots use a cancellation-resistant equivalent.
Reference Sources
Frequently asked questions
How does this calculator work?
D=b²−4ac; x=(−b±sqrt(D))/(2a). Coefficients are divided by their largest absolute value before computing the displayed normalized discriminant. Distinct real roots use a cancellation-resistant equivalent.
What assumptions should I check?
Check the units and definitions shown beside each input. Results use the values you enter.
Can I save or print this calculation?
Use Copy link with inputs to reproduce the scenario, Download results for a text record, or Print. Where a schedule is shown, its CSV download includes every row.