Answer
The solutions are $x=\dfrac{1}{9}$ and $x=-\dfrac{5}{2}$
Work Step by Step
$\dfrac{5}{x^{2}}-\dfrac{43}{x}=18$
Multiply the whole equation by $x^{2}$:
$x^{2}\Big(\dfrac{5}{x^{2}}-\dfrac{43}{x}=18\Big)$
$5-43x=18x^{2}$
Take all terms to the right side of the equation and rearrange:
$0=18x^{2}+43x-5$
$18x^{2}+43x-5=0$
Solve by factoring:
$(2x+5)(9x-1)=0$
Set both factors equal to $0$ and solve each individual equation for $x$:
$2x+5=0$
$2x=-5$
$x=-\dfrac{5}{2}$
$9x-1=0$
$9x=1$
$x=\dfrac{1}{9}$
The solutions are $x=\dfrac{1}{9}$ and $x=-\dfrac{5}{2}$
