When is the first equation used to calculate pressure change in a system?

[FollowTheFez]

I am going through old exam questions about pressure and fluid dynamics.
For one particular question I had to calculate the change in pressure in a system. These two equations were given on the formula sheet:

ΔP=$\frac{4\gamma}{R}$

and

ΔP=$\frac{2\gamma}{R}$


I've never seen the equation with the '4' in it. I've only every used the second equation to calculate pressure change (and always got answers correct). I can't find the first equation anywhere in my textbook or study guide.
I was wondering if someone could briefly explain when you would use that equation?

I am assuming that it's got something to do with where the pressure difference is only half (e.g. half a bubble sitting on top of water)?

 

[Chestermiller]

The first equation applies to a thin film bubble, like a soap bubble. The second equation applies to a bubble of gas within a body of surrounding liquid.