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