> You need to understand the fundamental difference between solving 
> x^2=2 for x

I think the solution is -1.4142135623730950488016887242097.
Let's see.
   -1.4142135623730950488016887242097 *
   -1.4142135623730950488016887242097 = 2.
Yep, I'm right.

> and applying the function sqrt(2). the sqrt is DEFINED as being positive.

Is it?
if x = [-b +/- sqrt(b^2 - 4ac]/2a, is b always positive?