Mathematics · Algebra
Quadratic Formula Calculator
Solve ax² + bx + c = 0 and inspect the discriminant.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Discriminant = -5² − 4(1)(6) = 1.
- √1 = 1.
- Substitute ±1 to obtain x = 3 and x = 2.
Definition and formula
The discriminant determines whether the equation has two, one or no real solutions.
x = (−b ± √(b² − 4ac)) ÷ 2a
Worked example
For x² − 5x + 6 = 0, the discriminant is 1 and the roots are 2 and 3.
Common mistake
The entire numerator, including −b and the square-root term, is divided by 2a.
How to learn with this calculator
Begin with the worked example, then change one value while keeping the others fixed. Compare the new result and calculation steps to identify which part of the formula changed.
Clear answers
Frequently asked questions
What does the Quadratic formula do?
Solve ax² + bx + c = 0 and inspect the discriminant.
How does the Quadratic formula work?
The calculator applies x = (−b ± √(b² − 4ac)) ÷ 2a. The discriminant determines whether the equation has two, one or no real solutions.
What can I learn from the Quadratic formula?
It connects the mathematical rule to your chosen numbers and shows each calculation step. Change one input at a time to see how the result responds.
Does MW SysArc receive or store what I enter?
No. The calculation runs locally in your browser. MW SysArc does not receive or store your calculation inputs.
How should I use the result?
Use the steps to understand the method, then verify important school or professional work using the notation and rounding rules required in your setting.
Last reviewed 2026-07-14. Calculations tested 2026-07-14.