# How do you solve 30x^2-5x=60?

May 21, 2017

$x = \frac{3}{2} ,$
$x = - \frac{4}{3}$

#### Explanation:

The contributor below solved it by factoring, here I'll solve it using my favourite method for quadratic equations : The Quadratic Formula.

So, like the contributor above, divide the entire equation by 5.
$6 {x}^{2} - x = 12$
Subtract 12 from both sides.
$6 {x}^{2} - x - 12$
Here is where we deviate from the factoring method : We take $a = 6 , b = - 1 , c = - 12$
And substitute it into the quadratic formula which is : $\frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$
You'll get :
$\frac{- \left(- 1\right) \pm \sqrt{{\left(- 1\right)}^{2} - 4 \cdot 6 \cdot - 12}}{2 \cdot 6}$
Simplify
$\frac{1 + \sqrt{1 + 288}}{12}$

$\frac{1 + \sqrt{289}}{12}$

$\frac{1}{12} + \frac{\sqrt{289}}{12} , \frac{1}{12} - \frac{\sqrt{289}}{12}$

$\frac{1}{12} + \frac{17}{12} , \frac{1}{12} - \frac{17}{12}$

$\frac{18}{12} , - \frac{16}{12}$

$\frac{3}{2} , - \frac{4}{3}$