\(14\dfrac{1}{2}-\dfrac{2\left(x+3\right)}{5}=\dfrac{3x}{2}-\dfrac{2\left(x-7\right)}{3}\)
\(\Leftrightarrow\dfrac{29}{2}-\dfrac{2x+6}{5}=\dfrac{3x}{2}-\dfrac{2x-14}{3}\)
\(\Leftrightarrow\dfrac{435-6.\left(2x+6\right)}{30}=\dfrac{45x-10\left(2x-14\right)}{30}\)
\(\Leftrightarrow435-12x-36=45x-20x+140\)
\(\Leftrightarrow37x=259\)
\(\Leftrightarrow x=7\)