Internals melting, please help

Need some help and I am not sure what I am doing wrong here. I am basing my work off this video of with a GGW and NBv4:
https://www.youtube.com/watch?v=v7BdiKfMkro&t=511s

For the GGW, just like the video, I have the two positive green LEDs wired in parallel and attached to one .5ohm 3W Resistor, as the video suggested I also used a .5ohm 3W resistor on my W FOC positive pad. The result is this, the resistor to the FOC positive pad overheats like crazy, to the point that the solder is coming off the joint. I've tried switching it to a 1.2 ohm 3W resistor but with the same result ... is this the result of my beginner soldering skills or am I missing something here?

Also, I am using a 3.7 Trustfire Li-Ion2400 mah battery.

Each LED should have its own resistor.

Okay I can get that, is that a difference between the NB3 that the video shows how to wire and the NB4? Because according to the math (that I am still learning with Omh's Law) the Forward Voltage of the green's are around 3.7 and the white is 3.1, so with a 3.7V battery I didn't think EACH LED would need a resistor ...

I’d have to research the various wiring diagrams, but I don’t think so. You add the resistor to help protect the LEDs themselves, and also, a 50 cent resistor is way cheaper than replacing a GGW Tri-Cree and/or melting internals. ;)

Agreed. But I guess where I am having trouble wrapping my mind around it is that when I to the math I come up with a negative value for R:

Vfbattery = 3.7
Green LED#1 FV=3.7
Green LED #2 FV=3.7 so
R= 3.7- (3.7+3.7)
R= 3.7 - (7.4)
R= -3.7/I where I=1
R=-3.7omhs

And then for the wattage:
P=R*I^2
P=-3.7 * 1^2
P= -3.7 watts??

I know that this is all new to me, but I can't figure out what to do with these negative values because the LED calculator gives me something different ....

You should use 4v for the battery. Full is 4.2 and although conventional wisdom says it drops quickly, that isn't true for modern batteries.

There it no such thing as negative current or resistance. I'm not sure what your math is supposed to be, but it's not right. Can you explain what formulas you think you are using?

Thanks,
So from what I understand Omh's law to be is V=I*R, so
R=V/I, but in this case we need the Voltage difference between the battery and the LED's forward voltage, so V= BatteryVoltage -(LED#1 Forward Voltage + LED #2 Forward Voltage), plugging in the numbers for a Green Green White Tri Cree (Green Forward voltage is 3.7 @ 1000ma) I got the following R=3.7 -(3.7+3.7)/1 --> R = (3.7 - 7.4)/1 n--> R = -3.7/1 --> R=-3.7 omhs ....

what did I do in correctly?

That's not how the math works. What you've approximated here is saying you are trying to pour two liters of water out of a one liter bottle. If you go over your budget you just don't get any more. You cannot run two 3.7v LEDs in series on a 3.7v source. In this case the LEDs just wouldn't light at all, they might not even conduct.

You need to calculate independently for each LED you are running in parallel. Some people don't bother putting a resistor on the green LED because of it's relatively high Vf, but I recommend against that practice. Do your math based on 4v.