The formula is ##N_t = N_0e^-((_1 + _2)t)##.
For a single decay mode the formula for decay rate is
##-(dN)/(dt) = N##
If there are two different simultaneous decay processes the total decay rate is the sum of the two processes.
##-(dN)/(dt) = _1N + _2N = (_1 + _2)N##
On integration this becomes
##N_t = N_0e^-((_1 + _2)t)##
We can simplify this by defining a new total decay constant ##_c##:
##_c = _1 + _2##
Then the equation becomes
##N_t = N_0e^-(_ct)##