[meekaaku]

To build a chart of accounts, you can have a parent column in accounts table. Account balances is just:

SELECT account.name, SUM(amount) balance

FROM account ac

INNER JOIN transaction_line tl ON tl.account_id = ac.id

GROUP BY account.name

You can cache this balance values with a current_balance column on accounts table

Once you have that, for any real world transaction, all you need to figure out is what are the accounts to debit/credit, ie classification. That is a higher level thing and is the business logic of an accounting application.