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Quadratic Formula Calculator
Use this quadratic formula calculator to solve any quadratic equation in the form ax² + bx + c = 0. Enter the values of a, b, and c to get the exact roots instantly.
This quadratic equation solver calculates both real and complex solutions and shows the steps used to reach the answer.
Quadratic Formula
x = (-b ± √(b² – 4ac)) / (2a)
This formula is used to solve quadratic equations where a is not zero.
How to Use the Quadratic Formula Calculator
Enter the value of a
This is the coefficient of x² and must not be zero.
Enter the value of b
This is the coefficient of x.
Enter the value of c
This is the constant term.
Click the Calculate button
This quadratic roots calculator will instantly compute the solution.
View the result
You will see the roots along with the steps used to solve the equation.
Example of Quadratic Formula
Solve:
x² + 5x + 6 = 0
a = 1
b = 5
c = 6
Result:
x = -2, -3
How to Solve a Quadratic Equation Using the Formula
Step 1: Identify the coefficients
a = 1, b = 5, c = 6
Step 2: Calculate the discriminant
b² – 4ac = 25 – 24 = 1
Step 3: Apply the quadratic formula
Step 4: Simplify the result
√1 = 1
Step 5: Find both solutions
x = (-5 + 1) / 2 = -2
x = (-5 – 1) / 2 = -3
Final answer:
x = -2, -3
When to Use the Quadratic Formula
Use the quadratic formula calculator when the equation cannot be factored easily or when you need exact solutions.
It works for every quadratic equation where a is not zero. It also handles cases where the solutions are complex.