Not to be cynical, but this technique has been known for years (although I can't find where it is documented in the curriculum). This idea is documented in any textbook on linear ordinary differential equations (ODEs) as a solution method where b and c are actually functions. However, there is a central (average) function that crosses the axis (which is when the equation becomes "homogeneous"). Also, the technique breaks down though when the function a becomes "singular" (i.e. equal to zero) at specific points and you are just left with a 1st order ODE solution at that point (or points) which is even easier to solve with integration techniques. Also, this solution requires more cognitive ability than guess/check then moving directly to the quadratic formula. So, while it seems novel, it doesn't really help anybody in the "general sense" because it only works for quadratic equations. The general ODE case I mentioned above works with functions that aren't necessarily even "symmetric" - meaning the center point +/-z are not the same value. Given all that, I'm not sure how stuff like this makes it into journal papers.