Answer
The solutions are $x=-2$ and $x=\dfrac{5}{4}$
Work Step by Step
$\dfrac{2x}{x-2}=5+\dfrac{4x^{2}}{x-2}$
Multiply the whole equation by $x-2$:
$(x-2)\Big(\dfrac{2x}{x-2}=5+\dfrac{4x^{2}}{x-2}\Big)$
$2x=5(x-2)+4x^{2}$
Evaluate the indicated operations:
$2x=5x-10+4x^{2}$
Take $2x$ to the right side and simplify:
$0=5x-10+4x^{2}-2x$
$0=4x^{2}+3x-10$
Rearrange:
$4x^{2}+3x-10=0$
$(x+2)(4x-5)=0$
Set both factors equal to $0$ and solve each individual equation for $x$:
$x+2=0$
$x=-2$
$4x-5=0$
$4x=5$
$x=\dfrac{5}{4}$
The solutions are $x=-2$ and $x=\dfrac{5}{4}$