Find all solutions to the equation.

7 sin^2x - 14 sin x + 2 = - 5

7sin²x-14sin x+2=-5

7sin²x-14sin x+7=0

Then: sin x=t

7t²-14t+7=0

We have to solve this square equation:

t=[14⁺₋√ (196-196) ]/14=14/14=1

t=1 ⇒sin x=1

x=sin⁻¹ 1=π/2 + 2kπ (k = ... - 3,-2,-1,0,1,2,3 ...)

For example:

if K=0 ⇒ x=π/2

7 (sin²π/2) - 14sin π/2+2=7 (1) ²-14 (1) + 2=7-14+2=-5

Answer: x=π/2 + 2kπ (k is an integer)