Question 312174
Okay from 
3 cos2x = cosx +2
let's apply our identity for cos 2x...
cos 2x = cos^2 x - sin^2 x = 2 cos^2 x - 1
so that if we substitute we get
3(2 cos^2 x - 1) = cos x + 2
6 cos^2 x - 3 = cos x + 2
6 cos^2 x - cos x - 5 = 0  now factor this...
(6 cos x + 5)(cos x - 1) = 0
and then
cos x = -5/6  or  cos x = 1
x = arc cos (-5/6)  or  x = 0