\(\displaystyle\frac{{x}}{{5}}-\frac{{1}}{{2}}=\frac{{x}}{{6}}\)

\(\displaystyle{x}\frac{{{6}}}{{5}}{\left({6}\right)}-{1}{\left(\frac{{15}}{{2}}{\left({15}\right)}={x}\frac{{{5}}}{{6}}{\left({5}\right)}\right)}\)

\(\displaystyle{6}\frac{{x}}{{36}}-\frac{{15}}{{36}}={5}\frac{{x}}{{36}}\)

\(6x-15=5x\)

\(x-15=0\)

\(x=15\)