Answer
$$x=\frac{1}{9}, -\frac{5}{2}$$
Work Step by Step
$$\frac{5}{x^2}-\frac{43}{x}=18$$
$$\frac{5}{x^2}-\frac{43x}{x^2}=18$$
$$\frac{5-43x}{x^2}=18$$
$$5-43x=18x^2$$
$$0=18x^2+43x-5$$
$$0=18x^2+(45x-2x)-5$$
$$0=9x(2x+5)-1(2x+5)$$
$$(9x-1)(2x+5)=0$$
$$x=\frac{1}{9}, -\frac{5}{2}$$
