Is it possible to make a non-inverting amplifier with positive feedback?
If you do that the amplifier will amplifiy its own output and the ouput will go high or low and stick there until a sufficiently low or high input is presented, which will make it go the other way (low or high).

In essence you will have created a schmitt trigger.

What the formulas don't show is that the solution for this amplifier configuration describes the metastable point, 

Another limitation of those equations is that they don't represent the limited output voltage range of real amplifiers.