Perhaps I'm misunderstanding you somewhere; but this is basically what I do for a living, so I don't think I'm wrong. I have carefully re-read my comments above, and would urge you to do the same.
Again: Can you write the quadratic formula in the way that you think is better (in pseudocode, or a language of your choice), and give examples of inputs where it performs better than floating point? If you don't do this and I'm wrong, then you're missing the opportunity to teach me (and all the people I'm misleading with my comments) something. If I'm right, then you're missing the opportunity to learn something yourself.
Again: Can you write the quadratic formula in the way that you think is better (in pseudocode, or a language of your choice), and give examples of inputs where it performs better than floating point? If you don't do this and I'm wrong, then you're missing the opportunity to teach me (and all the people I'm misleading with my comments) something. If I'm right, then you're missing the opportunity to learn something yourself.