Quadratic Formula Calculator
Solve quadratic equations using the quadratic formula
About this calculator
The Quadratic Formula Calculator solves quadratic equations of the form ax² + bx + c = 0 using the quadratic formula x = (-b ± √(b²-4ac)) / 2a. This powerful tool instantly finds both real and complex solutions, eliminating the need for manual calculations that are prone to arithmetic errors. It's essential for students, engineers, and professionals who need quick, accurate solutions to quadratic equations in algebra, physics, engineering, and other mathematical applications.
How to use
Enter the coefficients a, b, and c from your quadratic equation ax² + bx + c = 0 into the respective input fields. Click the calculate button to instantly get both solutions (x₁ and x₂). The calculator will show the discriminant value and indicate whether solutions are real or complex.
Frequently asked questions
What is the discriminant and why does it matter?
The discriminant is b²-4ac. If positive, there are two real solutions; if zero, one real solution; if negative, two complex solutions.
Can this calculator solve equations with complex solutions?
Yes, the calculator handles all cases including complex solutions when the discriminant is negative, displaying results with imaginary components.
What if the coefficient 'a' is zero?
If a=0, the equation becomes linear (bx + c = 0), not quadratic. The calculator will indicate this isn't a quadratic equation.