\(\Leftrightarrow2015x+\left(1+2....+2015\right)=2015.2016\)
\(\Leftrightarrow2015x+\dfrac{\left(1+2015\right).2015}{2}=2015.2016\)
\(\Leftrightarrow2015x=-\dfrac{2016.2015}{2}+2015.2016\)
\(\Leftrightarrow2015x=\dfrac{2016.2015}{2}\)
\(\Leftrightarrow x=1008\)