If a, b, c are particular values, example a = 1 b = 2 c = 3 then the equations above DO NOT have the same solution set. I never claimed the 2 forms above have the same solution set for PARTICULAR values.
If you consider a, b, c, abstractly, as running through all real numbers then the 2 forms above have the same solution set. TAKEN AS A WHOLE SET. I emphasize this last part because it is very important for the definition and derivation that I did.
To post 1 example would not be enough. I have to post 7, to show the way signs effect both formulas, a total of 14 calculations. I have been dreading this but i will do it. Give me some time.
My argument was the textbook definition and formula has more symbols than my version so that makes my version simpler.