[tex] \bf \cfrac{4}{2(x-3)}=\cfrac{5}{3(14-x)}\implies \stackrel{\textit{distributing in the denominators}}{\cfrac{4}{2x-6}=\cfrac{5}{42-3x}}
\\\\\\
4(42-3x)=5(2x-6)\implies \stackrel{\textit{distributing again}}{168-12x=10x-30}\implies 198=22x
\\\\\\
\cfrac{198}{22}=x\implies \boxed{9=x} [/tex]
