Answer
The solution is $n=\frac{3}{2}$.
Work Step by Step
$n\sqrt2=\sqrt 9-3n$
Square both sides:
$2n^2=9-3n$
$2n^2+3n-9=0$
$(2n-3)(n+3)=0$
$2n-3=0$ or $n+3=0$
$n=\frac{3}{2}$ or $n=-3$
Check:
$n\sqrt2=\sqrt 9-3(\frac{3}{2})$
$\frac{3}{2}\sqrt2=\frac{3\sqrt 2}{2}$
$(-3)\sqrt2=\sqrt 9-3(-3)$
$-3\sqrt2=3\sqrt2$
The solution is $n=\frac{3}{2}$.
