# How do you solve  7x^2+2x-2=0 using the quadratic formula?

Oct 19, 2015

$x = \frac{- 1 \pm \sqrt{15}}{7}$

#### Explanation:

Given a quadratic equationin the form:
$\textcolor{w h i t e}{\text{XXX}} \textcolor{red}{a} {x}^{2} + \textcolor{b l u e}{b} x + \textcolor{g r e e n}{c} = 0$
the quadratic formula tells us that the solutions are:
$\textcolor{w h i t e}{\text{XXX}} x = \frac{- \textcolor{b l u e}{b} \pm \sqrt{{\textcolor{b l u e}{b}}^{2} - 4 \textcolor{red}{a} \textcolor{g r e e n}{c}}}{2 \textcolor{red}{a}}$

Given
$\textcolor{w h i t e}{\text{XXX}} \textcolor{red}{7} {x}^{2} + \textcolor{b l u e}{2} x + \textcolor{g r e e n}{- 2}$
this becomes
$\textcolor{w h i t e}{\text{XXX}} x = \frac{- \textcolor{b l u e}{2} \pm \sqrt{{\textcolor{b l u e}{2}}^{2} - 4 \cdot \textcolor{red}{7} \cdot \textcolor{g r e e n}{\left(- 2\right)}}}{2 \cdot \textcolor{red}{7}}$

$\textcolor{w h i t e}{\text{XXXXX}} = \frac{- 1 \pm \sqrt{15}}{7}$