# How do you solve 3x^2=x+4 by factoring?

Oct 26, 2016

$x = 1 \frac{1}{3}$, $- 1$

#### Explanation:

$3 {x}^{2} = x + 4$

Shift all the terms to the left.

$3 {x}^{2} - x - 4 = 0$

Factorise.

$3 {x}^{2} + 3 x - 4 x - 4 = 0$

$3 x \left(x + 1\right) - 4 \left(x + 1\right) = 0$

$\left(3 x - 4\right) \left(x + 1\right) = 0$

$3 x - 4 = 0$ and $x + 1 = 0$

$x = \frac{4}{3} = 1 \frac{1}{3}$ and $x = - 1$