Choose the one alternative that best completes the statement or answers the question.
Solve the equation.
-$$4 x - 5 = \frac { 3 } { x }$$
A) $\left\{ \frac { 5 \pm \sqrt { 73 } } { 8 } \right\}$
B) $\left\{ \frac { 5 \pm \sqrt { 73 } } { 4 } \right\}$
C) $\left\{ \frac { 5 \pm \sqrt { 37 } } { 8 } \right\}$
D) $\left\{ \frac { 5 \pm \sqrt { 37 } } { 4 } \right\}$

Question

Quizplus · Accepted Answer

To solve the equation $4x - 5 = \frac{3}{x}$, multiply both sides by $x$ to get rid of the fraction: $4x^2 - 5x - 3 = 0$. Then, use the quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ with $a = 4$, $b = -5$, and $c = -3$. This gives $x = \frac{5 \pm \sqrt{(-5)^2 - 4(4)(-3)}}{2(4)} = \frac{5 \pm \sqrt{25 + 48}}{8} = \frac{5 \pm \sqrt{73}}{8}$, which matches choice A.

Choose the One Alternative That Best Completes the Statement or Answers