$\frac{100}{x}-\frac{100}{x+20}=\frac{5}{12}$
$\frac{100}{x}-\frac{100}{x+20}-\frac{5}{12}=0$
$\Leftrightarrow \frac{100.12(x+20)-100.12x-5x(x+20)}{12x(x+20)}=0$
$\Leftrightarrow 1200x+24000-1200x-5x^{2}-100x=0$
$\Leftrightarrow 5x^{2}+100x-24000=0$
$\Leftrightarrow x^{2}+20x-4800=0$
$\Leftrightarrow x^{2}-60x+80x-4800=0$
$\Leftrightarrow x(x-60)+80(x-60)=0$
$\Leftrightarrow (x-60)(x+80)=0$
$\Leftrightarrow \left[ \begin{array}{l}x-60=0\\x+80=0\end{array} \right.$
$\Leftrightarrow \left[ \begin{array}{l}x=60\\x=-80\end{array} \right.$
