Is there a mistake in which formula to use when buying certain amount of X tokens ?

[falcon-lin-development]

this says

we can always find the input amount using the Δx formula (when we want to buy a known amount of tokens).

But in fact, what we need to do is to switch place of x and y and still use the Delta(y) formula?

Reason:

1. we need to take account into the transaction fee.
2. Buying Token X is essentially selling the Token Y.

Please correct me if I'm wrong

[0xkaranchauhan]

@falcon-lin-development
No need to switch the variables x and y and use the Δy formula. Instead, use the provided formulas as intended:

• To find the output amount of token y when selling a known amount of token x, use Δy = (yrΔx) / (x+rΔx).
• To find the input amount of token x needed to buy a known amount of token y, use Δx = (xΔy) / (r(y−Δy)).
  These formulas already incorporate the transaction fees and respect the relationships between supply and demand.

[falcon-lin-development]

I see it now. Thanks a lot.