If you wright:
What do you notice?
cos^2 x + 3 cos^2 x+2=0
4 cos^2 x = -2
cos^2 x = -1/2
cos x = plus or minus -1/2
x lies in the 1st, 2nd, 3rd and 4th quadrant since it has positive and negative values. Now find the basic angle and solve for the 4 possible angles.