Quadratic Equation Calculator
What are the real solutions of ax squared plus bx plus c equals zero? Enter the values below to calculate the result.
Result for the values shown.
Calculations run in your browser.
What to enter
| Input | Meaning and units |
|---|---|
| Coefficient a | Enter coefficient a using the definition in the method and example. |
| Coefficient b | Enter coefficient b using the definition in the method and example. |
| Coefficient c | Enter coefficient c using the definition in the method and example. |
Understanding your result
Read Discriminant, Root using minus sign, Root using plus sign in the units and model stated on this page. The formula D=b*b-4*a*c · x1=(-b-sqrt(max(0,D)))/(2*a) · x2=(-b+sqrt(max(0,D)))/(2*a) defines the relationship; measurement accuracy and model applicability are separate from numerical precision.
Common mistakes
- Using a different mathematical definition or operation than the one stated by this tool.
Check your calculation
- Use the worked example as a known reference case, then change one input at a time and check the direction and units of the response.
Calculation checks, sources and review limits
What are the real solutions of ax squared plus bx plus c equals zero?
What are the real solutions of ax squared plus bx plus c equals zero? Enter the values below to calculate the result.
Common uses
- What are the real solutions of ax squared plus bx plus c equals zero
How it works
D=b*b-4*a*c; x1=(-b-sqrt(max(0,D)))/(2*a); x2=(-b+sqrt(max(0,D)))/(2*a)
Worked example
Enter Coefficient a: 1 ; Coefficient b: -5 ; Coefficient c: 6 . Results: Discriminant: 1 ; Root using minus sign: 2 ; Root using plus sign: 3 .