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

### Notes

A quadratic equation is any equation that can be written as: ax

^{2} + bx + c = 0, where x is unknown, and a, b, and c are constants. The constants a and b are called coefficients. Further, it should be mentioned that a cannot equal 0 in the equation ax

^{2}+bx+c=0. Otherwise, the equation ceases to be a quadratic equation, and becomes a linear equation.

Finding a solution to a quadratic equation may appear daunting, because both x and x

^{2} are unknown. Fortunately, you have this handy-dandy quadratic equation calculator. Acutally, quadratic equations can be readily solved using the

quadratic formula, which is the same technique used by this quadratic equation calculator. Try it, and it will explain each of the steps to you. The quadratic formula is written:

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 the same, producing one solution for x.

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

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 calculator 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.