Equity is automatically calculated using the formula, total assets less total liabilites. Anytime anything changes in assets or liabilities total equity will change.

A Nonprofit should IMO use funding accounts. A bank account for the following
Operational
restricted (one for each kind of restriction)
unrestricted

All transactions happen in the operational account
then money is moved out of the operational account and into either a restriced account or an unrestricted account.
The same thing happens when you pay out money, transfer the funds to the operational account, then make the payment.