# How do I find all solutions for? 5 sqr 3 tan+3 = 8 sqr 3 tanx

Feb 10, 2018

$\textcolor{b l u e}{\frac{\pi}{6} + n \pi}$

#### Explanation:

$5 \sqrt{3} \tan x + 3 = 8 \sqrt{3} \tan x$

$3 = 8 \sqrt{3} \tan x - 5 \sqrt{3} \tan x$

$3 = 3 \sqrt{3} \tan x$

Divide by 3:

$\sqrt{3} \tan x = 1$

$\tan x = \frac{1}{\sqrt{3}}$

$x = \arctan \left(\tan x\right) = \arctan \left(\frac{1}{\sqrt{3}}\right) = \frac{\pi}{6} + n \pi$

Where $n$ is an integer.