#### Answer

$n=1.5$

#### Work Step by Step

$n\sqrt2 = \sqrt {9-3n}$
$(n\sqrt2)^2 = (\sqrt {9-3n})^2$
$n^2*2 = 9-3n$
$2n^2=-3n+9$
$2n^2+3n-9=-3n+9+3n-9$
$2n^2+3n-9 = 0$
$(2n-3)(n+3)=0$
$2n-3=0$
$2n=3$
$2n/2 = 3/2$
$n=1.5$
$n+3=0$
$n=-3$
$n=-3$
$n\sqrt2 = \sqrt {9-3n}$
$-3*\sqrt2 = \sqrt {9-3(-3)}$
$-3*\sqrt2 = \sqrt {9+9}$
$-3*\sqrt2 = \sqrt {18}$
$-3*\sqrt2 = \sqrt {3*3*2}$
$-3*\sqrt2 \ne 3\sqrt 2$
$n=1.5$
$n\sqrt2 = \sqrt {9-3n}$
$1.5*\sqrt2 = \sqrt {9-3*1.5}$
$1.5\sqrt2 = \sqrt {9-4.5}$
$1.5\sqrt2 = \sqrt {4.5}$
$1.5\sqrt2 = \sqrt 9/\sqrt2$
$1.5\sqrt2 = \sqrt 9/\sqrt2*(\sqrt2/\sqrt2)$
$1.5\sqrt2 = 3\sqrt2/2$
$1.5\sqrt2 =1.5\sqrt2$