When should we use delta formuls in an equation?

Answer 1

When we want to know the rate of change of something. For instance, speed is a change in distance divided by change in time. In other words: If x_1 is your starting position, x_2 is your ending position, t_1 is your starting time and t_2 is your ending time, then your speed is:
(x_2 - x_1) / (t_2 - t_1) or you could say delta x over delta t.

Answer 2

The greek letter delta is used in math and science whenever referring to change - especially in derivative calculus.

Answer 3

if you mean the discriminant (delta=(b^2-4ac)^1/2) in the Q.E. it is to know the nature of the roots.