Let's call field a "debit", field b "credit" and field c, "cBal".
Define cBal as a calculation field with a number result type and this expression: Debit - Credit.
Now define a summary field: sBalance as the running total of cBal
In a list or table view, you can get a view of your data where each record is a row with these fields. The cBal field need not be present on the layout if you don't need it.
This is a standard "bookkeeping ledger" type solution (hence the field names that I used here and in this demo file that I created some time ago: https://dl.dropboxusercontent.com/u/78737945/AccountingLedger.fmp12