It’s not clear if the equation is 7sin²(x)-14sin(x)+2=-5 or 7sin(2x)-14sin(x)+2=-5.
Assuming it’s the former to start with we have:
So the solution is sin(x)=1, from which x=π/2, 5π/2, 9π/2, or, in general terms, π/2+2nπ=(4n+1)π/2 where n is any positive or negative integer, including 0. This gives x in radians. In degrees this is 90(4n+1).
This is the most likely solution and interpretation of the question.