we have that
2sin²x - sinx - 3 = 0
Let
A------> sin x
so
2A²-A-3=0
using a graph tool-----> to resolve the second order equation
see the attached figure
the solutions are
A=-1
A=1.5------> is not solution because sin x can not be 1.5
the solution is
A=-1
therefore
sin x=-1
x=arc sin(-1)=-90°
the answer is
sin x=-1
x=-90° or 270°