# How do you solve  2x(x - 1) = 3?

Mar 26, 2016

$x = \frac{1 \pm \sqrt{13}}{4}$

#### Explanation:

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

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

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

Comparing with $a {x}^{2} + b x + c = 0$ we get,

$a = 4 , b = - 2 , c = - 3$

By Formula method,

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

$x = \frac{- \left(- 2\right) \pm \sqrt{{\left(- 2\right)}^{2} - 4 \times 4 \times - \left(3\right)}}{2 \times 4}$

$x = \frac{2 \pm \sqrt{4 + 48}}{8}$

$x = \frac{2 \pm \sqrt{52}}{8}$

$x = \frac{2 \pm \sqrt{4 \times 13}}{8}$

$x = \frac{2 \pm \sqrt{4 \times 13}}{8}$

$x = \frac{2 \pm 2 \sqrt{13}}{8}$

$x = \frac{2 \left[1 \pm \sqrt{13}\right]}{8}$

$x = \frac{1 \pm \sqrt{13}}{4}$