After 86 posts, we still haven't posted exactly what Delta-X is and how it, the ISO standard, and the fractional gradient relate.
ISO Speed Graph with Delta X equatioin.jpg
The contrast parameters of the ISO speed standard provides the ΔD variable in the Delta-X criterion. The log-H range from the speed point is 1.30 but from the fractional gradient point is Δ1.50, which is what it is in the fractional gradient method. So, the ISO speed standard is in essence a single fractional gradient situation. The fixed density of 0.10 over Fb+f always has a Δ0.29 from the fractional gradient speed point. It stands in as an easy to find substitute for the trial and error method of determining the shadow gradient of the fractional gradient method. Because the ΔX value is known and unchanging under the ISO contrast parameters, use of the Delta-X equation isn't required. It's built in. If the processing conditions do happen to vary, only then is it necessary to use the equation.
Once again, the methodology is only important in determining the speed point that most closely correlates to the print judgment speed first determined in the first excellent print tests by Jones. Film speed and/or EI is then calculated from the speed point using a speed constant which is based on the desired placement of the luminance values in conjunction with the exposure meter. Exposure meters are designed to place the metered exposure at 8/ISO. Knowing the ratio between the speed point and the metered exposure point creates an understanding of where the average exposure will fall which is how the speed constant is determined. The value of the constant can be the one used in the ISO standard, or an equivalent one with the Delta-X Criterion, or one that is personalized. But whatever the it is, all are based on the same characteristic curve criteria.