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

You entered:

There are two real solutions: x = 0.62422813026934, and x = -1.6242281302693.

(1)

For any quadratic equation

(2)

In the form above, you specified values for the variables a, b, and c. Plugging those values into Eqn. 1, we get:

(3) \(x=-72\pm\frac{\sqrt{72^2-4*72*-73}}{2*72}\)

which simplifies to:

(4) \(x=-72\pm\frac{\sqrt{5184--21024}}{144}\)

\(x=\frac{-72+161.88885075878}{144}\) = 0.62422813026934,

and

\(x=\frac{-72-161.88885075878}{144}\) = -1.6242281302693,

Both of these solutions are real numbers.

These are the two solutions that will satisfy the quadratic equation

Solving a linear equation is straightforward. Solving a quadratic equation requires more work. However, you have this handy-dandy quadratic equation solver. All kidding aside, quadratic equations can be quickly solved using the quadratic formula, which is the same technique used by this quadratic equation solver. 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. Rarely, the two roots may be equal, producing one solution for x.

Quadratic equations have real-life applications. Quadratic equations are needed to calculate answers in many real-world fields, including engineering, pharmacokinetics and architecture.

The quadratic equation calculator on this website uses the quadratic formula to solve your quadratic equations, and this is a reliable and relatively simple way to do it. But there are other ways to solve a quadratic equation, such as completing the square or factoring.

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 we totally understand if you just want to use it to find the answers you're looking for. Thank you for your interest in Quadratic-Equation-Calculator.com.

click here for a random example of a quadratic equation.