Derivation of stable spot price

I'm trying to ascertain the correctness of the function that calculates the stable spot price. Referring to the code [here](https://github.com/balancer/balancer-v2-monorepo/blob/903d34e491a5e9c5d59dabf512c7addf1ccf9bbd/pkg/pool-stable/contracts/meta/StableOracleMath.sol#L46). 

1. how is this equation derived? 
2. why is that `S` (sum of balances) is 0?