[tex]\displaystyle x+2x+3x+...+2015x=1+2+3+...+2014 \\ \\ x(1+2+3+...+2015)= \frac{2014(2014+1)}{2} \\ \\ x \cdot \frac{2015(2015+1)}{2} = \frac{2014 \cdot 2015}{2} \\ \\ x \cdot \frac{2015 \cdot 2016}{2} = \frac{4058210}{2} \\ \\ x \cdot \frac{4062240}{2} =2029105 \\ \\ x \cdot 2031120=2029105 \\ \\ x= \frac{2029105}{2031120} [/tex]
