\(\frac{18\cdot123+9\cdot436+2\cdot5310+6}{1+4+7+...+100-410}\)
\(=\frac{18\cdot123+18\cdot436+18\cdot885+6}{\frac{\left(\frac{\left(100-1\right)}{3}+1\right)}{2}\cdot\left(100+1\right)-410}\)
\(=\frac{18\cdot\left(123+436+885\right)+6}{1717-410}\)
\(=\frac{18\cdot1444+6}{1307}\)
\(=19,89\)