#### Answer

$x=100$ or $x=-50$

#### Work Step by Step

$\displaystyle \frac{x^{2}}{x+100}=50$
We cross-multiply:
$x^{2}=50(x+100)$
And distribute:
$x^2=50x+5000$
$x^{2}-50x-5000=0$
And solve by factoring:
$(x-100)(x+50)=0$
$x-100=0$ or $x+50=0$
$x=100$ or $x=-50$