# Solving 27x2+-94x+73 using the Quadratic Formula

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

For your equation of the form "ax2 + bx + c = 0," enter the values for a, b, and c:

 a x2 + b x + c = 0
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You entered:
27x2+-94x+73=0.

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

## Here's how we found that solution:

You entered the following equation:
(1)           27x2+-94x+73=0.

For any quadratic equation ax2 + bx + c = 0, one can solve for x using the following equation, which is known as the quadratic formula:
(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)           $$x=--94\pm\frac{\sqrt{8836-7884}}{54}$$

Now, solving for x, we find two real solutions:
$$x=\frac{--94+30.854497241083}{54}$$ = 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 27x2+-94x+73=0.

### Notes

A quadratic equation is any equation that can be written in the form: ax2 + bx + c = 0, where x is an unknown, and a, b, and c are constants. A and b are referred to as coefficients. Interestingly, a cannot equal to 0 in the equation ax2+bx+c=0.

Finding a solution to a quadratic equation may appear daunting, because both x and x2 are unknown. 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:

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, both roots may be equal, producing one solution for x.

Quadratic equations are an important part of mathematics. Quadratic equations are needed to find answers in many real-world fields, including physics, pharmacokinetics and business.

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.

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