I received this link from some friend in math department some minutes ago. According to the email, there has been quite a rumble about this talk.
This
http://www.mozaik.info.hu/Homepage/ftp/gondolkozzunk_gorogul/geom.html
or this link if you are not an English speaker: mozaik homepage
Author: Andras Ringler
Head of the Institute of Medical and Biophysics, University of Szeged (Hungary)
While I am not really impressed with this claimed new discovery, this clip is actually nice and quite helpful to draw attention from students in junior high school. I still remembered when I was in the 8th grade and was so excited to learn many “tricks” to solve equations and even more excited trying to explain why it could work and rediscover the real meaning behind the methods.
Nevertheless, just flash back the way the well-known quadratic formula was formed (or the formula itself is a hint), you can “discover” a much nicer and intuitive geometrical solution, using similarities (in a right triangle) that dont even have to separate +/- in to cases. Give it a try.