Ok, to start I converted the delta on the outside to a star configuration, which gave me resistances of 5 Ω for each leg. Since they are now star, they are in parallel with the original star and can be combined. After combining all of the star resistances I have 1 star configuration where each leg has a resistance of 4, as seen in my 2nd attachment.

At this point I'm thinking that I can put the legs of the star in series with the legs that arent in the star configuration to get 3 resisances of 8, 10, and 10Ω, as seen in attachment 3.

Now I'm not exactly what to do because of the 2 emfs. Any point in the right direction would be greatly appreciated. Thanks.

 

You haven't told us what the goal of the problem is. If you read the "sticky" post at the beginning of this forum, you will find that one of the things you're supposed give us is: "A description of your homeworks objectives."

Are you supposed to determine the current in each of the resistors? Or, is there some other goal?

What methods of circuit analysis are you supposed to use? Can you use any method you wish? What methods have you studied?

 

Oh sorry, I'm supposed to find the current I.

 

Nevermind, I figured it out

 

You didn't answer my further question:

"What methods of circuit analysis are you supposed to use? Can you use any method you wish? What methods have you studied?."

Have you studied the method of superposition? I think that might be the most appropriate method for this problem, after your delta-star transformations.

If you have, try to apply it and show your efforts.