# How do you solve 3x^2 - 15x=0 using the quadratic formula?

Nov 7, 2016

$x = 0 \textcolor{w h i t e}{\text{XX")orcolor(white)("XX}} x = 5$

#### Explanation:

Note: there are easier ways to solve this ...but since the quadratic formula was requested, here goes:

Remember the quadratic formula tells us that given a quadratic in 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 solutions are given by the formula
$\textcolor{w h i t e}{\text{XXX}} x = \frac{- \textcolor{b l u e}{b} \pm \sqrt{{\textcolor{b l u e}{b}}^{2} - 4 \textcolor{red}{a} \textcolor{g r e e n}{c}}}{2 \textcolor{red}{a}}$

Converting the given equation: $3 {x}^{2} - 15 x = 0$ into this form:
$\textcolor{w h i t e}{\text{XXX")color(red)3x^2+color(blue)(} \left(- 15\right)} x + \textcolor{g r e e n}{0} = 0$

The solutions are
color(white)("XXX")x=(-color(blue)(""(-15))+-sqrt((color(blue)(-15)^2-4 * color(red)3 * color(green)0)))/(2 * color(red)3)

$\textcolor{w h i t e}{\text{XXX}} = \frac{15 \pm \sqrt{{15}^{2}}}{6}$

$\textcolor{w h i t e}{\text{XXX")x=30/6=5color(white)("XX")orcolor(white)("XX}} x = 0$