Answer
$x=\displaystyle \frac{-3\pm\sqrt{41}}{8}$
Work Step by Step
$2x^{-2}-3x^{-1}-4=0$ ... multiply with $-x^{2}$
$-2+3x+4x^{2}=0$
$4x^{2}+3x-2=0$ ... use the quadratic formula.
$x=\displaystyle \frac{-3\pm\sqrt{9+32}}{8}=\frac{-3\pm\sqrt{41}}{8}$
$x=\displaystyle \frac{-3\pm\sqrt{41}}{8}$