We have the input voltage (PSE voltage) dividing between cable and load.
We get a quadratic equation from this
where a = 1, b = − VIN/Rcable, c = PPD/Rcable
We will have no solution if b2 is less than 4ac. And the two solutions converge when b2 equals 4ac. That is when
And since PPD = VPD2/RPD, we get VPD = VIN/2, and ...