Let the expression = x



Notice that the red expression is the same as the original 
expression, so



Square and isolate radicals until you end up with this 4th degree equation.



which factors by trial and error as



Setting each one equal to 0 and solving by the quadratic formula
gives 

 and 

The answer must be positive, so it is one of these:

 or 

The first one satisfies



but the second one does not.

Answer: 

Edwin