$(x- \frac{1}{2}).\frac{1}{6}+(x-\frac{1}{2}).\frac{1}{12}+(x-\frac{1}{2}).\frac{1}{20}+...+(x-\frac{1}{2}).\frac{1}{90}=\frac{19}{5}$
$(x-\frac{1}{2}).(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{90})=\frac{19}{5}$
$(x-\frac{1}{2}).(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{9.10})=\frac{19}{5}$
$(x-\frac{1}{2}).(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10})=\frac{19}{5}$
$(x-\frac{1}{2}).(\frac{1}{2}-\frac{1}{10})=\frac{19}{5}$
$(x-\frac{1}{2}).\frac{2}{5}=\frac{19}{5}$
$x-\frac{1}{2}=\frac{19}{2}$
$x=10$
