# How do you solve 2x^2 + 9x = 8 ?

Mar 17, 2016

Re-write the n equation in standard form then apply the quadratic formula

#### Explanation:

General standard form for a quadratic:
$\textcolor{w h i t e}{\text{XXX}} \textcolor{red}{a} {x}^{2} + \textcolor{b l u e}{b} x + \textcolor{g r e e n}{c} = 0$
Quadratic formula for roots:
$\textcolor{w h i t e}{\text{XXX}} x = \frac{- \textcolor{b l u e}{b} \pm \sqrt{{\textcolor{b l u e}{b}}^{2} - 4 \textcolor{red}{a} \textcolor{g r e e n}{c}}}{2 \textcolor{red}{a}}$

$2 {x}^{2} + 9 x = 8$
expressed in standard form:
$\textcolor{w h i t e}{\text{XXX}} \textcolor{red}{2} {x}^{2} + \textcolor{b l u e}{9} + \textcolor{g r e e n}{\left(- 8\right)} = 0$

Solutions:
$\textcolor{w h i t e}{\text{XXX}} x = \frac{- \textcolor{b l u e}{9} \pm \sqrt{{\textcolor{b l u e}{9}}^{2} - 4 \left(\textcolor{red}{2}\right) \left(\textcolor{g r e e n}{- 8}\right)}}{2 \left(\textcolor{red}{2}\right)}$

$\textcolor{w h i t e}{\text{XXXx}} = \frac{- 9 \pm \sqrt{145}}{4}$