2cos^2(X) - 3sin(X) = 0
2(1 - sin^2(X)) - 3sin(X) = 0
2 - 2sin^2(X) - 3sin(X) = 0
-2sin^2(X) - 3sin(X) + 2 = 0
-2sin^2(X) - 4sin(X) + sin(X) + 2 = 0
-2sin(X)(sin(X) + 2) + 1(sin(X) + 2) = 0
(-2sin(X) + 1)(sin(X) + 2) = 0
Solve First:
-2sin(X) + 1 = 0
sin(X) = -1/-2 = 1/2
Quadrant 1, 2
Ref. Angle PI/6
X1 = PI/6
X2 = PI - PI/6 = 5PI/6
Solve Second:
sin(X) + 2 = 0
sin(X) = -2
CANNOT ANSWER
X = PI/6, 5PI/6

You could have possibly went sin(X) = -1/2 or sin(X) = 1/-2 rather than sin(X) = -1/-2 = 1/2 ;)