\(\Leftrightarrow2018x^2-2018x+2019x-2019=0\\ \Leftrightarrow2018x\left(x-1\right)+2019\left(x-1\right)=0\\ \Leftrightarrow\left(2018x+2019\right)\left(x-1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=1\\2018x=-2019\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-\dfrac{2019}{2018}\end{matrix}\right.\)