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 function that takes the form: ax

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

^{2}+bx+c=0.

Solving a quadratic equation may appear daunting, because both x and x

^{2} are unknown. Fortunately, any quadratic equation can reliably be solved using the

quadratic formula. Here is the quadratic formula:

Since there are always 2 solutions to a square root (one negative, one positive), solving the quadratic equation results in 2 values for x. The two solutions for x (which may be positive or negative, real or complex) are called roots. Rarely, the two roots may equal each other, resulting in one solution for x.

Why do we care about qudratic equations? Quadratic equations are needed to compute answers in many real-world fields, including engineering, 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 this quadratic equation calculator is useful to you. 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.