I'm not sure what you mean "solve for," or "what the answer is called," but here's the deal with PPI.
Take the number of pixels along any side of your image. (E.g., if you have an 800x600 pixel image, you can use either the 800 side or the 600 side.) Now, divide that by the number of inches that side will be printed as. (E.g., if you're printing your 800x600 image as a 4"x3" picture, you will take 800/4 or 600/3 -- notice that both give you the same answer, 200.)
That number, pixels / inches (200 in our example) is the PPI for that PRINT. Remember, PPI is only relevant to a print! It is NOT an inherent feature of an image (despite much confusion to the contrary).
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