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

You entered:

There are two real solutions: x = 2.3121203192793, and x = 1.1693611622022.

(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) \(x=--94\pm\frac{\sqrt{-94^2-4*27*73}}{2*27}\)

which simplifies to:

(4) \(x=--94\pm\frac{\sqrt{8836-7884}}{54}\)

\(x=\frac{--94+30.854497241083}{54}\) = 2.3121203192793,

and

\(x=\frac{--94-30.854497241083}{54}\) = 1.1693611622022,

Both of these solutions are real numbers.

These are the two solutions that will satisfy the quadratic equation

Solving a linear equation is rather basic. Solving a quadratic equation is not as 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 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, these two roots may be the same, resulting in one solution for x.

There are many uses for quadratic equations. Quadratic equations are needed to find answers to many real-world problems. The laws of motion is one example of an application of quadratic equations.

The term "quadratic" comes from the Latin word

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