# How do you solve 12x^2 = 5x + 2?

Jun 24, 2016

$x = \frac{2}{3} , X = - \frac{1}{4.}$

#### Explanation:

$12 {x}^{2} = 5 x + 2. \Rightarrow 12 {x}^{2} - 5 x - 2 = 0.$

Observe that, $8 \times 3 = 24 , 8 - 3 = 5.$

Spliting $5 x$ as $8 x - 3 x , 12 {x}^{2} - 8 x + 3 x - 2 = 0.$
$\therefore 4 x \left(3 x - 2\right) + 1 \left(3 x - 2\right) = 0 ,$ or, $\left(3 x - 2\right) \left(4 x + 1\right) = 0.$

$\therefore 3 x - 2 = 0 , \mathmr{and} , 4 x + 1 = 0 ,$ giving, $x = \frac{2}{3} , X = - \frac{1}{4.}$