Just to check - are you back on the manual bookkeeping course?

First off - be very careful with your 'credit side of the equation' definition. EG income is mostly a credit entry - that much is true. BUT there are cicrumstances when a debit entry is required and the adjustments needed is just one example.

If you enter ONLY the debit balances then the TB will show an imbalance. So you would enter a suspense balance to make it balance and then you can then go off and hunt for the reason why.

If two things are entered on the debit side instead of one debit and one credit - you will get an imbalance.

Re your example (1)

I bought office equipment for 500 pounds and paid with debit card. I have an increase on assets account for 500 pounds ( account with debit balance ) and decrease on bank account for the same amount ( account with debit balance ).

The debit card entry will be a credit balance. But if you debited it in error then you would have to correct the original wrong entry (so 1 x £500 credit entry to the Bank) and then enter the correct credit entry (so a secoond £500 credit entry via the Bank). Your balancing entry will be the suspense account, the opposite of where you would have posted to get the TB to balance in the first place.

Re your example (2)
Office equipment Dr 500 Bank Cr 50

So here you will have an imblanace of £450 on the TB. So you would have to move that to suspense so your TB balances (credit suspense £450). Then to correct it - credit bank with the difference £450 and debit suspense £450.

Always either draw it up as a mini TB. Or better still - write it down in three ways via a T account:-

1) What you did (the wrong oway)
2) What entries you should have done
then
3) What you need to do to put it right.

As you work through this T account process it becomes plainer how to correct it.

Glad I asked - the think with sage is:-

The only time you can really have two non balancing double entries such as the ones you mention is if you try to use the journal entry method. This though would flag up that they dont balance and ouldnt let you post them until they are balanced. Besides the fact that for most entries you would not be doing it via the journal screen.

Usually when you are say using the Bank screen - you will be eg paying for an item. So take your purchase of office equipment - on the bank payment option you would enter it as £500 to be paid from the bank. Then you choose the fixed asset nominal code and the £500 is auto posted to that account.

You can go wrong so care is an absolute must with Sage, but its rare you will encounter the situations you mention above.