$x+1/\sqrt[]{5x+2}+(x+2)(\sqrt[]{5x+2})=9/\sqrt[]{5x+2}$ $Đkxđ:x\neq-2/5$
$⇔(x+2)(\sqrt[]{5x+2})=9/\sqrt[]{5x+2}-x+1/\sqrt[]{5x+2}$
$⇔(x+2)(\sqrt[]{5x+2})=10-x/\sqrt[]{5x+2}$
$⇔(x+2)(\sqrt[]{5x+2})^2=10-x$
$⇔(x+2)(5x+2)=10-x$
$⇔5x^2+2x+10x+4=10-x$
$⇔5x^2+13x=6$
$⇔x(5x+13)=6$
$⇔\left[ \begin{array}{l}x=0\\5x+13=0\end{array} \right. ⇔\left[ \begin{array}{l}x=0(tmđkxđ)\\x=-13/5(tmđkxđ)\end{array} \right.$
Vậy $S=${$0;-13/5$}.