# How do I solve 3 tan^2 x - sec^2 x -5 = 0?

Nov 20, 2017

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

#### Explanation:

Multiply both sides by ${\cos}^{2} x$
So we get,
$3 {\sin}^{2} x - 1 - 5 {\cos}^{2} x = 2 {\sin}^{2} x - 6 {\cos}^{2} x = 0$
So,
$2 {\sin}^{2} x = 6 {\cos}^{2} x$

${\tan}^{2} x = 3$
$\tan x = \sqrt{3}$
$x = \frac{\pi}{3}$