3sin²x + 1/2 sin2x = 2

3 sin(x)^2 + (1/2) sin(2x) = 2
2 - 3 sin(x)^2 = (1/2) sin(2x)
2 - 3 sin(x)^2 = sin(x) cos(x)
[ 2 - 3 sin(x)^2 ]^2 = sin(x)^2 [ 1 - sin(x)^2 ]
Обозначим sin(x)^2 = t
[ 2 - 3t ]^2 = t (1 - t)
4 - 12 t + 9 t^2 = t - t^2
10 t^2 - 13 t + 4 = 0
D = 9
t = (13 (+\-) 3) / 20
t1  = 4/5
t2 = 1/2

sin(x)^2 = t1
sin(x)^2 = 4/5
sin(x) = (+\-) 2/sqr(5)
x = (+\-) arcsin(2/sqr(5)) + пк

sin(x)^2 = t2
sin(x)^2 = 1/2
sin(x) = (+\-) sqr(2)/2
x = п/4 + пk/2