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

### Notes

A quadratic equation is any equation that takes the form: ax

^{2} + bx + c = 0, where x is a variable which is not known, and a, b, and c are constants. A and b are referred to as coefficients. Interestingly, a cannot be zero. Otherwise, the equation ceases to be a quadratic equation, and becomes a linear equation.

Solving a linear equation is straightforward. Solving a quadratic equation is less simple. Fortunately, there are a number of methods for solving quadratic equations. One of the most widely used is the

quadratic formula. The quadratic formula is:

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. Depending on the values of a, b, and c, these two roots may have the same value, producing one solution for x.

Quadratic equations are important. Quadratic equations are needed to compute answers in many real-world fields, including physics, pharmacokinetics 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 this quadratic equation calculator is useful to you. We encourage you to plug in different values for a, b, and c. But, if you just want to use it to calculate the answers to your quadratic equations, that's cool too. Thank you for your interest in Quadratic-Equation-Calculator.com.

click here for a random example of a quadratic equation.