# How do you solve 5x ^ { 2} + 9x - 20= 4- 5x?

May 30, 2018

Rearrange the expression so one side equals zero, then use the quadratic formula to find $x = \left\{- 4 , 1.2\right\}$

#### Explanation:

First, we'll rearrange the expression so the Right Hand Side (RHS) equals zero. This will give us our quadratic expression to use in the quadratic formula:

$5 {x}^{2} + 9 x - 20 \textcolor{red}{- 4} \textcolor{b l u e}{+ 5 x} = \cancel{4} \textcolor{red}{\cancel{- 4}} \cancel{- 5 x} \textcolor{b l u e}{\cancel{+ 5 x}}$

$5 {x}^{2} + 9 x \textcolor{b l u e}{+ 5 x} - 20 \textcolor{red}{- 4} = 0$

$5 {x}^{2} + 14 x - 24 = 0$

Now, we'll utilize The Quadratic Formula. For any quadratic expression that looks like $a {x}^{2} + b x + c$:

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

For this case:

$a = 5$
$b = 14$
$c = - 24$

Let's plug that in:

$x = \frac{- 14 \pm \sqrt{\left({14}^{2}\right) - 4 \left(5\right) \left(- 24\right)}}{2 \left(5\right)}$

$x = \frac{- 14 \pm \sqrt{196 - 4 \left(- 120\right)}}{10}$

$x = \frac{- 14 \pm \sqrt{196 + 480}}{10}$

$x = \frac{- 14 \pm \sqrt{676}}{10}$

$x = \frac{- 14 \pm 26}{10}$

$x = \left\{\frac{- 14 - 26}{10} , \frac{- 14 + 26}{10}\right\}$

$x = \left\{\frac{- 40}{10} , \frac{12}{10}\right\}$

$\textcolor{g r e e n}{x = \left\{- 4 , 1.2\right\}}$