Question

Is it possible for someone to make this algorithm easy to understand to enter into a calculation for my application.

Thanks

To explain:

Answer 1

Yes that algorithm most certainly can be expressed in a programming language, however I will not provide an implementation, but some pseudocode to get you started.
So the first thing we see is x is dealing with money so lets represent that as a double

double monthlyPayment //this is X

next we see that P sub 0 is the total loan amount so lets also represent that as a double

double loanAmount // this is P sub 0  

next we see that i is the interest rate so this will also be a double

double interestRate // this is i

next we see that n is the number of months that remain on the loan this is an integer

int monthsRemaining // this is n

so looking at the formula you proposed we take the following:

monthlyPayment = (loanAmount * interestRate) /  1 - (1 + interestRate) ^ (-1 * monthsRemaining)

Now without actually implementing this I do believe you can take it from here.