15(sinx + 1)^2 = 17 + 31sinx
15(sin^2x + 2sinx + 1) = 17 + 31sinx
15sin^2x + 30sinx + 15 = 17 + 31sinx
15sin^2x + 30sinx + 15 - 17 - 31sinx = 0
15sin^2x - sinx - 2 = 0
sinx=t, t ∈ [ - 1; 1]
15t^2 - t - 2 = 0
D = 1 + 4*30 = 121
t1 = ( 1 + 11)/30 = 12/30 = 2/5
t2 = ( 1 - 11)/30 = - 10/30 = - 1/3
sinx = 2/5
x = (-1)^k arcsin (2/5) + pik. k ∈Z
sinx = - 1/3
x = (-1)^(k+1) arcsin(1/3) + pik. k ∈Z