Solve `sqrt(5-2 sin x)=6 sin x-1`

Explanation

The equation is meaningful if `sin x le 5/2` which is always true.
Any x for which `sin x lt 1/6` cannot be solution, since `sqrt(5-2 sin x gt 0)` for all x.
On squaring the equation, we get
`5-2 sin x =36 sin^(2) x-12 sin x+1`
or `18 sin^(2) x-5x-2=0`
`:. (9 sin x+2)(2 sin x-1)=0`
`:. sin x=-2/9 or sin x=1/2`
But `sin x=-2/9` is not possible `" "( :' sin x lt 1/6" is not possible")`
`:. sin x=1/2`
`rArr x=n pi +(-1)^(n) pi/6, n in Z`