Question

Solve 8 = 36sin^2 3x+60sin3x+17, where x {0,2pi}

Answer 1

let p = sin 3 x

then
36 p^2 + 60 p + 9 = 0
12 p^2 + 20 p + 3 = 0
(2 p + 3) ( 6 p - 1) = 0
p = 1/6 if it is to be sin of something
sin 3 x = 1/6
Your turn :)

Answer 2

Thanks!