# How do you solve y = x^2 - 6x + 8 = 0 using the quadratic formula?

May 9, 2018

Use the coefficients with the formula, and you will find that $x = \left\{2 , 4\right\}$

#### Explanation:

The Quadratic Formula is written as follows:

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

Where the quadratic equation used looks like this:

$a {x}^{2} + b x + c = 0$

Using this pattern, we can see the following:

$a = 1$
$b = - 6$
$c = 8$

Let's plug these numbers into the formula:

$x = \frac{- \left(- 6\right) \pm \sqrt{{\left(- 6\right)}^{2} - 4 \left(1\right) \left(8\right)}}{2 \left(1\right)}$

$x = \frac{6 \pm \sqrt{36 - 32}}{2}$

$x = \frac{6 \pm \sqrt{4}}{2} = \frac{6 \pm 2}{2} = 3 \pm 1$

$x = \left\{\begin{matrix}3 - 1 \\ 3 + 1\end{matrix}\right\}$

color(green)(x={2,4}