Chapter 1 - Section 1.4 - Radical Equations; Equations Quadratic in Form; Factorable Equations - 1.4 Assess Your Understanding - Page 118: 70

$x=\displaystyle \frac{-3\pm\sqrt{41}}{8}$

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