# How do you solve 2x^2+3x-3=0 using the quadratic formula?

Mar 17, 2016

$x = \frac{- 3 + \sqrt{33}}{4}$ or $x = \frac{- 3 - \sqrt{33}}{4}$

#### Explanation:

For a quadratic in the general standard 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 for the solution(s) is
$\textcolor{w h i t e}{\text{XXX}} x = \frac{- \textcolor{b l u e}{b} \pm \sqrt{{\textcolor{b l u e}{b}}^{2} - 4 \left(\textcolor{red}{a}\right) \left(\textcolor{g r e e n}{c}\right)}}{2 \left(\textcolor{red}{a}\right)}$

For the given equation: $\textcolor{red}{2} {x}^{2} + \textcolor{b l u e}{3} x \textcolor{g r e e n}{- 3}$
color(white)("XXX")x=(-color(blue)(3)+-sqrt(color(blue)(3)^2-4(color(red)(2))(color(green)(-3))))/(2(color(red)(2))
color(white)("XXX")x=(-color(blue)(3)+-sqrt(color(blue)9+24))/(2(color(red)(2))
$\textcolor{w h i t e}{\text{XXX}} = \frac{- 3 \pm \sqrt{33}}{4}$