\(\left(x-1\right)+\left(x-2\right)+...+\left(x-100\right)=50\)
\(x.100-\left(1+2+...+100\right)=50\)
\(x.100-\left(\left(100+1\right).100:2\right)=50\)
\(x.100-\left(101.100:2\right)=50\)
\(x.100-5050=50\)
\(x.100=50+5050\)
\(x.100=5100\)
\(x=5100:100\)
\(x=51\)