what is the general equation for half-life?
Strictly speaking, a half-life is a number with dimensions of time, not an equation. It's value depends upon what the material is.
If you meant to ask what is the amount N of material remaining After time t, in terms of half life T, then
N(t)/No = (1/2)^(t/T)
T is the half life in this equaton, and No is the amount of the radioactive material at time 0.