A free quadratic equation calculator that shows and explains each step in solving your quadratic equation.

### Notes

What is a quadratic equation? A quadratic equation is an equation ax

^{2} + bx + c = 0. In this equation, x is a variable of unknown value. A, b, and c are constants. The constants a and b, are referred to as coefficients. It should be mentioned that a cannot be zero. If a=0, then ax

^{2}=0, and the equation becomes 0+bx+c=0, or bx+c=0. The equation bx+c=0 is a linear equation, and not a quadratic equation.

Solving a quadratic equation can seem challenging. However, there are a number of methods for solving quadratic equations. One of the most widely used is the

quadratic formula. This is the quadratic formula:

Solving a quadratic equation will always result in 2 solutions for x. These solutions are called roots. These roots may both be real numbers or, they may both be complex numbers. Under extraordinary circumstances, these two roots may be equal, resulting in one solution for x.

Why do we care about qudratic equations? Quadratic equations are needed to find answers in many real-world fields, including physics, biology and business.

As mentioned above, in the equation ax

^{2}+bx+c=0, a cannot be zero. If a were 0, then ax

^{2} = 0x

^{2} = 0 for any value of x, so our equation becomes 0 + bx + c = 0, which is the same as bx + c = 0, which is no longer a quadratic equation. In fact, bx + c = 0 is a linear equation, which is much simpler to solve than a quadratic equation.

We hope you find this quadratic equation solver useful. We encourage you to try it with different values, and to read the explanation for how to reach your answer. But, if you just want to use it to calculate the answers to your quadratic equations, that's cool too. Thank you for using Quadratic-Equation-Calculator.com.

click here for a random example of a quadratic equation.