# What are the solutions to the equation? 2x^2 - x = 3

Mar 30, 2018

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

#### Explanation:

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

By sum and product

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

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

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

Now either $x = - 1$ or $x = \frac{3}{2}$

The $x = - 1$ doesn't satisfy the equation whereas $x = \frac{3}{2}$ does.

=$2 {\left(\frac{3}{2}\right)}^{2} - \left(\frac{3}{2}\right)$

=$\frac{9 - 3}{2}$

=$3 = 3$ Hence proved

Hope this helps!