The Kandelhardt Paradox

Speaking of real paradoxes, here's one I just found. If you know much about algebra, or math for that matter, you can go through and see that the above steps to solve for the equation 25-45=16-36 is accurate. Each step follows the accepted rules of math, which I'm sure you all know (Pythagorean theorem, anyone?) Most of you would say, why not just subtract and get -20=-20? That works, but so does the solution above, until you get to the actual solving part. It's a fact that 5 does not equal 4. But this equation, found by the mathematician Kandelhardt, says otherwise. Maybe one can actually argue with a mathematical equation, Stephan Hawking.Actually there is a rather simple solution to this, at leats, simple for all you math nerds. As Ralph Buchholz from Ralph the Triangle puts it:

The step from the third last line to the second last line requires a square root.
This has two possible solutions, namely positive or negative. The temptation
to equate the two positive roots is overwhelming—and wrong. Equating the
opposite sign roots gives the correct answer. Ultimately, squaring and taking square roots are not inverses of each other.

You can see the equation for the solution here.