Answer
$x=-\frac{1}{9}$ or $x=-1$
Work Step by Step
We simplify as follows:
$\sqrt{-10x-1}+3x=0$
$\sqrt{-10x-1}=-3x$
$-10x-1=9x^{2}$
$9x^{2}+10x+1=0$
$(9x+1)(x+1)=0$
$9x+1=0$ or $x+1=0$
$9x=-1$ or $x=-1$
$x=-\frac{1}{9}$ or $x=-1$
