# How do you solve the equation (x-2)^2/4+3/2=5/3?

Aug 20, 2017

$2 \pm \frac{2}{\sqrt{6.}}$

#### Explanation:

We have, ${\left(x - 2\right)}^{2} / 4 + \frac{3}{2} = \frac{5}{3} ,$

$\therefore {\left\{\frac{x - 2}{2}\right\}}^{2} = \frac{5}{3} - \frac{3}{2} = \left\{\frac{5 \cdot 2 - 3 \cdot 3}{3 \cdot 2}\right\} = \frac{1}{6} ,$

$\therefore \frac{x - 2}{2} = \pm \sqrt{\frac{1}{6}} ,$

$\therefore x - 2 = \pm \frac{2}{\sqrt{6}} ,$

$\therefore x = 2 \pm \frac{2}{\sqrt{6.}}$