Find the value of X where 2 + 9√x/(2√3 -√3x)=√3+2√2

Answer 1

3√3/(√x-2) + 2√3 + √2 = 1
√x = 2 + 3√3/(1 - 2√3 - √2)
x = (2 + 3√3/(1 - 2√3 - √2))^2
Now, since 1/(1 - 2√3 - √2) = (-13 + 11√2 - 18√3 + 4√6)/73
that gives
x = (13945 - 8874√2 + 6000√3 - 3864√6) / 5329