This equation I like more than the "beatiful" equation () mainly becaus it's not that mysterious. There is certain propoties of the quadractic equation that can be looked at and tested.
1st one is what shape will the equation be:
Is the shape of:
And The second property you can get is directly from the quadractic equation, whether a equation has 2 roots, 1 root or it has imaginary roots
How many roots has this equation got?
Okay that was fun hope you enjoy.