6sin^2x=5sin (3pi/2-x) + 2

6 sin^2 x = 5 sin (3pi/2 - x) + 2;

6 sin^2 x = - 5 cos x + 2;

6 sin^2 x + 5 cos x - 2 = 0;

6 (1 - cos^2 x) + 5 cos x - 2 = 0;

6 - 6 cos^2 x + 5 cos x - 2 = 0;

6 cos^2 x - 5 cos x - 4 = 0;

D = 25+144 = 121 = 11^2;

cos x = (5+11) / 12 = 16/12 = 4/3 > 1; нет решений.

сos x = - 1/2; x = + - pi/3 + 2pi*k; k-Z