Table 3 shows the math needed to get Delta neutral strikes. P.a. stands for premium adjusted which is also explained in the paper.

It is a very good paper to read.
Equity VOL surfaces are fundamentally different. Generally, derived from listed option prices (with all complexities involved in that).
FX is relatively simple. ATM Delta neutral Straddles (DNS), Risk Reversals (RR) and Butterfly (BF) quotes completely describe the entire surface. ATM the level, RR the skew and BF the kurtosis. There are some complications like premium included / excluded Delta, Delta style (spot vs forward), spread models used etc but equity is generally more complicated with de-Americanizing option prices, finding implied forwards and dividends and the like.
Delta neutral is neat in itself. In terms of the strike, it's simply the K such that
call delta = - put delta
Take a simple example with assumes premium excluded:
Days to expiry = 30
Vol = 8%
Fwd = 1.25
$$Fwd*exp^{0.5*(Vol/100)^2*(days/365)} = 1.2503$$
Daycount may vary obviously. Could be ACT/365 or BD/252 (commonly used in BRL) for example.
On a side remark, it's interesting that you have a closed-form solution for Delta as well as Strike with premium adjusted delta. However, going from Delta to strike itself is not possible and would require a root solver in this case.
To get actual vols for calls and puts, one needs to transform these and solve for call / put vol.
RR = Vol of an OTM Call Option (C) - Vol of an OTM Put Option (P)
BF = ( C + P ) / 2 - Vol of ATM DNS
it's simple to show that
C = ATM + BF + RR/2
P = ATM + BF - RR/2
where you get say a 25 Delta call if you use 25D RR and BF respectively.
The above uses smile BF but brokers frequently quote market BF (short broker fly). These are a bit more involved and have equal notional strangle strikes whereas the notional on the ATM straddle is set such that the package is initially vega neutral. FX Volatility smile construction by Dimitri Reiswich and Uwe Wystup explains this in more detail (if this link does not work anymore, it can be searched easily).