#### Answer

$x=9$ and $x=1$

#### Work Step by Step

$\sqrt{16x}=x+3$
Square both sides of the equation:
$(\sqrt{16x})^{2}=(x+3)^{2}$
$16x=x^{2}+6x+9$
Take $16x$ to the right side of the equation and simplify it by combining like terms:
$0=x^{2}+6x-16x+9$
$x^{2}-10x+9=0$
Solve this equation by factoring:
$(x-9)(x-1)=0$
Set both factors equal to $0$ and solve each individual equation:
$x-9=0$
$x=9$
$x-1=0$
$x=1$
Check the answers found by substituting them into the original equation:
$x=9$
$\sqrt{16(9)}=9+3$
$12=12$ True
$x=1$
$\sqrt{16(1)}=1+3$
$4=4$ True
The final answers are $x=9$ and $x=1$