What do you mean with "ideal and simple equation"? I think we can do assay of most of pharmaceuticals by using RP-HPLC; you can search the method of HPLC determination for any pharmaceuticals in Google, Scopus, or other data base. If you have the column, mobile phase and suitable detector (UV, DAD,ELSD, MS or others), than you can apply in your laboratory, after optimization you can do validation of the method.
If I am not wrong, then I guess you are searching this equation to find out the assay result of your sample preparation:
Assay = (Peak area of sample / Peak area of standard) X (Amount of standard taken / volume of standard solution) X (Volume of sample solution / Amount of sample taken) X (Potency of standard / 100) X Dilution factor X Conversion factor
Do you mean equation above as "equation for calculation of sample"?
For using equations that described by Subrata and Harshal above (=single point calibration) to calculate the concentration of sample/test, some requirements should be fulfilled (see the book from J. Ermer & P. Nethercote (Eds.) Method Validation in Pharmaceutical Analysis, Wiley-VCH, 2015, pp.146, 158). See Table 5.14
1. Linear regression function should be proved (r, Vxo, Mandel etc should have acceptance value)
You can read the method development in different kinds of HPLC techniques, especially haw you can manipulate the practical factors basing upon some theoretical factors such as retention factor k, selectivity factor, and number of theoretical plates N, you can find these topics in detail in Quantitative chemical analysis by D. C. Harries.