Answer
$x=12$
Work Step by Step
Isolate the square root on one side. Then square both sides and put all terms on one side. Factor by trial and error to solve for $x$. One of the answers does not work.
$\sqrt {3x}+10=x+4$
$\sqrt {3x}=x-6$
$(\sqrt {3x})^2=(x-6)^2$
$3x=x^2-12x+36$
$x^2-15x+36=0$
$(x-3)(x-12)=0$
$x=3,12$
$\sqrt {3\times3}+10\ne3+4$
$x=12$