4cosx + 3 = 0

I assume we are solving.

4cosx = -3
cosx = -3/4
x must be in quadrants II or III by the CAST rule
the reference angle is 41.4°
(I took arccos .75)

so x = 180-41.4 = 138.6°
or x = 180+41.4 = 221.4°

set your calculator to radians if you want the answer in radians