# How do you solve 12y^2-5y=2?

May 20, 2016

The solution is:
color(blue)(y=2/3, y=-1/4

#### Explanation:

$12 {y}^{2} - 5 y = 2$

$12 {y}^{2} - 5 y - 2 = 0$

The equation is of the form color(blue)(ay^2+by+c=0 where:

$a = 12 , b = - 5 , c = - 2$

The Discriminant is given by:

$\Delta = {b}^{2} - 4 \cdot a \cdot c$

$= {\left(- 5\right)}^{2} - \left(4 \cdot 12 \cdot \left(- 2\right)\right)$

$= 25 + 96 = 121$

The solutions are normally found using the formula
$= \frac{- b \pm \sqrt{\Delta}}{2 \cdot a}$

$y = \frac{- \left(- 5\right) \pm \sqrt{121}}{2 \cdot 12} = \frac{5 \pm 11}{24}$

$y = \frac{5 + 11}{24} = \frac{16}{24} = \frac{2}{3}$

$y = \frac{5 - 11}{24} = - \frac{6}{24} = - \frac{1}{4}$