Answer
$x=25$
Work Step by Step
$\sqrt{10+3\sqrt{x}}=\sqrt x\\(\sqrt{10+3\sqrt{x}})^2=(\sqrt x)^2\\10+3\sqrt{x}=x\\10-x=-3\sqrt{x}\\(10-x)^2=(-3\sqrt{x})^2\\100+x^2-20x=9x\\x^2-29x+100=x^2-4x-25x+100=x(x-4)-25(x-4)=(x-4)(x-25)=0$
Thus $x=4$ or $x=25$ but the equation is undefined for the earlier, thus $x=25$