Answer
$x=-4$
Work Step by Step
By cross-multiplication, in terms of $x$, the given equation, $
\dfrac{3x-4}{2x}=-\dfrac{8}{x}
,$ is equivalent to
\begin{array}{l}\require{cancel}
-x(3x-4)=2x(8)
\\\\
-3x^2+4x=16x
\\\\
-3x^2+4x-16x=0
\\\\
-3x^2-12x=0
\\\\
-3(x^2+4x)=0
\\\\
x^2+4x=\dfrac{0}{-3}
\\\\
x^2+4x=0
\\\\
x(x+4)=0
\\\\
x=\{-4,0\}
.\end{array}
Upon checking, only $
x=-4
$ satisfies the original equation.
