This question is very unclear to me, and no attempts were made to improve the question. As Arthur said:
You start with $ax^2+bx+c = 0$, work through a whole lot of steps, and end with $ax^2+bx+c = 0$. Which is to say, you're back exactly where you started. What have you actually accomplished? What is it that you want to accomplish? — Arthuryesterday