Help me Please.

OK.....this looks a little daunting.....let's make it easier

Let     x /y  =  "a"

So     x^2 / y^2  =  (x /y)^2   =  "a^2"

Now.....we have someting that is a little more familiar....so....

4 (x^2/y^2)   - 36 (x/y)  + 81        becomes

4a^2  -  36a  + 81        let us guess that the factorization of this is

(2a - 9) (2a - 9)          verify for yourself that this is the correct factoring

(2a - 9)^2

But.....also ....notice that   

[ -(2a - 9) ]  [ - (2a - 9) ]    will also produce the same result  = [ - (2a - 9) ]^2

So......the square roots  are

±(2a - 9)       ....so....just back-substitute and we have

± [ 2(x/y) - 9 ]