divide ax^2+bx+c=0 by x^2 on both sides. what is the new equation?

ax² + bx + c = 0

Divide the equation by x² on the both sides:
(ax² + bx + c)/x² = 0/x²

The new equation is:
a + (b/x) + (c/x²) = 0

Put 1/x = y, the new equation can also be written as:
a + by + cy² = 0, where y = 1/x