"An interesting question is why nobody has stumbled across and widely shared this method before" Hmmmm... I "discovered" this method when I was like 14, but I

"An interesting question is why nobody has stumbled across and widely shared this method before" Hmmmm... I "discovered" this method when I was like 14, but I didn't think it was a big deal, since it was equivalent to the standard formula. I'm very sure that I'm not among the first million people who "discovered" this on their own. Also, while this allows some quick calculations in your head (the example equation, x^2-2x+4=0, is certainly faster to do with this method than with the standard formula), for more complicated equations it loses it appeal very quickly, especially if the main coefficient is greater than one (think of something like 3x^2+2x+1=0, which is still not very complicated, and you will realise the usefulness of the standard formula). As someone who has loved math since forever and who has discovered a million of "neat tricks" like this one (mostly useless, though), I've sometimes wondered whether some of them could actually be useful. Over the years it has become clear that all the "neat tricks" that are actually neat and useful are indeed widely shared everywhere, while the not so neat remain obscure despite being relatively easy to be discovered, because they don't have much application. And people like me who are willing to spend the time rediscover them again and again, only to discard them because they aren't a big deal. An example of an actually good trick: I was so proud of my novel algorithm to find the gcd of two numbers when I was in high school... then, in my first year at the university, I learned that it was called "Euclid's algorithm" and, as the name implies, it was pretty old :) .