Hey guys!

I need help solving the following trigonometric equation:

$\displaystyle 7 cos x = 4 - 2 sin^2 x$

I get:

$\displaystyle 7 cos x = 4 -2(1-cos^2 x)$

$\displaystyle 7 cos x = 4 -2 + 2 cos^2 x$

$\displaystyle 2 cos^2 x - 7 cos x + 2 = 0 $

It turns out this doesn't factor very well, and I'm almost sure I made a mistake. None of the problems I'm working on require the quadratic equation so I'm pretty sure that I just solved the equation incorrectly.

Help?