#### Answer

$x=\{2,10\}$

#### Work Step by Step

Multiplying both sides by the $LCD=
4x
,$ then the given equation, $
\dfrac{x}{4}+\dfrac{5}{x}=3
,$ simplifies to
\begin{array}{l}\require{cancel}
x(x)+4(5)=4x(3)
\\\\
x^2+20=12x
\\\\
x^2-12x+20=0
\\\\
(x-10)(x-2)=0
\\\\
x=\{2,10\}
.\end{array}
Upon checking, both solutions satisfy the original equation. Hence, there is $
x=\{2,10\}
.$