Answer
$x=\frac{1\pm\sqrt{33}}{8}$
Work Step by Step
$4-\displaystyle \frac{1}{x}-\frac{2}{x^{2}}=0$
We multiply by $x^2$:
$x^{2}(4-\frac{1}{x}-\frac{2}{x^{2}})=x^{2}*0$
$4x^{2}-x-2=0$
We solve using the quadratic formula ($a=4,\ b=-1,\ c=-2$):
$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
$x=\frac{-(-1)\pm\sqrt{(-1)^{2}-4*4*-2}}{2*4}$
$x=\frac{1\pm\sqrt{1+32}}{8}$
$x=\frac{1\pm\sqrt{33}}{8}$
