It is
$3\sin x+4\cos x=2 $
What I did is
$(3\sin x)^2=((2-4\cos x)^2$ to get
$9-9\cos^2x=4-16\cos x+16\cos^2 x$ then I got
$25\cos^2 x-16\cos x-5=0$
However I am having trouble finding the root I tried using the quadratic formula and got x=.866 I am not sure what I do wrong.