#### Answer

$x=1$ and $x=4$

#### Work Step by Step

$\sqrt{9x}=x+2$
Square both sides of the equation:
$(\sqrt{9x})^{2}=(x+2)^{2}$
$9x=x^{2}+4x+4$
Take the $9x$ to the right side of the equation and simplify it by combining like terms:
$0=x^{2}+4x-9x+4$
$x^{2}-5x+4=0$
Solve this equation by factoring:
$(x-1)(x-4)=0$
Set both factors equal to $0$ and solve each individual equation:
$x-1=0$
$x=1$
$x-4=0$
$x=4$
Check the answers found by substituting them into the original equation:
$x=1$
$\sqrt{9(1)}=1+2$
$3=3$ True
$x=4$
$\sqrt{9(4)}=4+2$
$6=6$ True
Our two final answers are $x=1$ and $x=4$