Whether you’re a student tackling algebra homework, a teacher preparing lessons, or a professional needing quick calculations, this quadratic formula calculator makes finding roots simple and accurate.
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Just enter the coefficients from your equation and get instant results, including both real and complex solutions.
What is the Quadratic Formula?
The quadratic formula is a mathematical equation used to find the solutions (also called roots or zeros) of any quadratic equation.
A quadratic equation is written in the standard form ax² + bx + c = 0, where a, b, and c are coefficients and x represents the unknown variable. T
his quadratic formula calculator applies the formula to find the values of x that make the equation true, giving you both solutions when they exist.
The Quadratic Formula
The quadratic formula is written as:
x = [-b ± √(b² – 4ac)] / (2a)
Where:
- a = coefficient of x²
- b = coefficient of x
- c = constant term
- ± means the formula produces two solutions: one using addition (+) and one using subtraction (-)
The expression under the square root symbol (b² – 4ac) is called the discriminant. Our quadratic formula calculator evaluates the discriminant to determine whether your equation has two real solutions, one real solution, or two complex solutions.
The discriminant (b² – 4ac) determines the number and type of roots:
- When b² – 4ac > 0, there are two distinct real roots
- When b² – 4ac = 0, there is one real root (a repeated root)
- When b² – 4ac < 0, there are two complex roots
Quadratic Formula Calculator
Quadratic Formula Example
Let’s use the quadratic formula calculator to solve the equation: 2x² + 5x – 3 = 0
Using the formula:
- a = 2, b = 5, c = -3
First, calculate the discriminant: b² – 4ac = (5)² – 4(2)(-3) = 25 + 24 = 49
Now apply the quadratic formula: x = [-5 ± √49] / (2 × 2) x = [-5 ± 7] / 4
This gives us two solutions: x = (-5 + 7) / 4 = 2/4 = 0.5 x = (-5 – 7) / 4 = -12/4 = -3
The solutions are x = 0.5 and x = -3. With our quadratic formula calculator, you can solve equations like this instantly without manually working through each calculation step, saving time and ensuring accuracy every time.
