`x-\sqrt{5x+4}=2`
⇔`x-2=\sqrt{5x+4}` `(x≥2)`
⇔`(x-2)^2=(\sqrt{5x+4})^2`
⇔`x^2-4x+4=5x+4`
⇔`x^2-4x-5x+4-4=0`
⇔`x^2-9x=0`
⇔`x(x-9)=0`
⇔\(\left[ \begin{array}{l}x=0\\x-9=0\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x=0(loại)\\x=9(tm)\end{array} \right.\)
Vậy `S={9}`