# How do you solve 5x^2-2x-6=-3x^2+6x?

Jun 27, 2017

$x = - \frac{1}{2}$, or $x = \frac{1}{2}$

#### Explanation:

First, let's add $3 {x}^{2}$ to both sides

$8 {x}^{2} - 2 x - 6 = 6 x$

Then, subtract $6 x$ from both sides

$8 {x}^{2} - 8 x - 6 = 0$

Divide the entire equation by $2$

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

Factorise

$\left(2 x + 1\right) \left(2 x - 3\right) = 0$

Set each factor equal to $0$

$2 x + 1 = 0$
$2 x = - 1$

$x = - \frac{1}{2}$

$2 x - 3 = 0$
$2 x = 3$
$x = \frac{1}{2}$

Here is the graph

graph{4x^2-4x-3 [-3.08, 3.08, -1.54, 1.54]}