$\dfrac{x-2}{4}=\dfrac{5+x}{3}$
$\to\dfrac{3(x-2)}{12}=\dfrac{4(5+x)}{12}$
$\to\dfrac{3x-6}{12}=\dfrac{20+4x}{12}$
$\to\dfrac{3x-6}{12}-\dfrac{20+4x}{12}=0$
$\to\dfrac{3x-6-20-4x}{12}=0$
$\to\dfrac{-x-26}{12}=0$
$\to-x-26=0$
$\to-x=26$
$\to x=-26$
Vậy $x=-26$.