\(\dfrac{x-2}{4}=\dfrac{5+x}{3}\Leftrightarrow\left(x-2\right).3=\left(5+x\right).4\)
\(\Leftrightarrow3x-6=4x+20\)
\(\Leftrightarrow3x=4x+20-6\)
\(\Leftrightarrow3x=4x+14\)
\(\Leftrightarrow3x-4x=14\)
\(\Leftrightarrow\left(-1\right).x=14\)
\(\Leftrightarrow x=-14\)