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

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

An equation that can be written as bx+c=0 is called a linear equation. It has one unknown, x, and 2 constants, b and c. If this equation were also to include the square of x as an unknown, it would become a quadratic equation. What is a quadratic equation? Any equation that can be written as: ax2 + bx + c = 0, where a, b, and c are constants. X is unknown. A and b are called coefficients. Further, a cannot be equal to zero in the equation ax2+bx+c=0. If a is 0, then ax2=0, and the equation becomes 0+bx+c=0, or bx+c=0. The equation bx+c=0 is a linear equation, and not a quadratic equation.

Solving a linear equation is relatively simple. Solving a quadratic equation is more complicated. 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. Depending on the values of a, b, and c, these two roots may be equal, resulting in one solution for x.