# How do you find the roots of 12x=9x^2+4 by factoring?

Oct 22, 2016

$x = \frac{2}{3}$

#### Explanation:

$12 x = 9 {x}^{2} + 4$

Subtract $12 x$ from both sides.

$0 = 9 {x}^{2} - 12 x + 4$ or $9 {x}^{2} - 12 x + 4 = 0$

Factorise the equation.

$9 {x}^{2} - 6 x - 6 x + 4 = 0$

$3 x \left(3 x - 2\right) - 2 \left(3 x - 2\right) = 0$

$\left(3 x - 2\right) \left(3 x - 2\right) = 0$

$3 x - 2 = 0$

$\therefore x = \frac{2}{3}$