nesting issue involving percentages

I have tried an array of math to the following percentage issue to no avail. I have 4 cells. 1 is for positive credits B10 and one is for total pool A10. In this case the goal is 70%. I have a cell A51 which subtracts B10 from A10 to give the total negatives. B51 is the kicker. I need to use the information above to determine how many have to be added to both the credit and the pool to get 70%. First I decided to use IF statements ie; IF(B10/A10)>.69,""(IF((B10+1)/(A10+1)>.69,1,(IF((B10+2)/(A10+2)>.69,2,(IF....and so on...this seems like stone wheel days to me and there must be an easier way..It will only let me go to 7 due to nesting issues anyway. Anyone know the correct math? If I started with 5 credits and 12 in the total pool (41.7%) I know that I would have to add 12 to both the credit and total pool or 17/24 to get to 70%. I would like cell B51 to indicate 12 needed to meet goal...help

Can I ask, given the 12, 5 & 70% rate why would the result be 9 ? Shouldn't it be 12 ?

12 + 9 = 21
5 + 9 = 14
14/21 -> 67% (thereabouts) - ie this fails the 70% limit

12 + 12 = 24
5 + 12 = 17
17/24 -> 71% (thereabouts) - ie this passes the 70% limit (11 does not)

I am sure there are ways for calculating this with math but in terms of a brute force method:

C51:
=MIN(IF(((B10+ROW(1:100))/(A10+ROW(1:100)))>=0.7,ROW(1:100)))
confirmed with CTRL + SHIFT + ENTER

the use of 100 is relative of course - and might need adjusting based on values in row 10

note the text in red / bold font in my prior post.

OK, being a doofus at this stuff I had to ask my Dad to give me the math:

Originally Posted by Dr D.O. PhD

(x+B1)/(x+A1)=p
where p is the percentage required

then
x+B1=px +p*A1

or

x(1-p)=p*A1-B1

so

x = (p*A1 - B1)/(1-p)

so this simplifies things significantly such that your function becomes:

=(0.7*A1-B1)/(1-0.7)

To round this value up to nearest whole integer we can either use ROUNDUP or CEILING, using the latter:

=CEILING((0.7*A1-B1)/(1-0.7),1)

This approach is obviously far more efficient than the Array.