# How do you solve 2x^2-x-6=0?

Jul 3, 2016

$x = 2 \mathmr{and} - \frac{3}{2}$

#### Explanation:

This is a quadratic so we expect to obtain two roots. Can recognise that we are able to factorise this to:

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

For the left hand side of the equation to equal zero, one of the brackets must evaluate to zero.

The first bracket:

$\left(2 x + 3\right) = 0 \implies x = - \frac{3}{2}$

The second:

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