Consider the lines that meet the graph $y = 2x^4 + 7x^3 + 3x - 5$ in four distinct points $P_i = (x_i, y_i), i = 1, 2, 3, 4$. Prove that $$\frac{x_1 + x_2 + x_3 + x_44}{4}$$ is independent of the line, and compute its value.