Putnam 1977 A1

Problem A-1 Consider all lines which meet the graph of $$y=2 x^{4}+7 x^{3}+3 x-5$$ in four distinct points, say $\left(x_{i}, y_{i}\right), i=1,2,3,4$. Show that $$\frac{x_{1}+x_{2}+x_{3}+x_{4}}{4}$$ is independent of the line and find its value.