What is the angle y if sin^2y=5siny-6 ?

sin^2 y = 5siny - 6

We will
move all terms to the left side so the right side is
0.

==> sin^2 y - 5siny + 6 =
0

Now let us assume that u=
siny

==> u^2 - 5u + 6 =
0

Let us factor.

==>
(u-2)(u-3) = 0

==> u= 2 ==> siny =
2 

==> u= 3 ==> siny =
3

Both solutions are invalid because the the values of sine
must be between -1 and 1.

==> -1 =< siny
=< 1

Then, the function has no
solution.