Third Equation!

Alright so!

This is our 3rd equation and third letter. 

This question was designed by UIntOverflow thank you so much! 

"Alice and Bob are hosting a party. They invite three couples to the party. At the party there are 8 people in total, including Alice and Bob. People at the party greet each other and shake hands. At the end of the party, Bob asked everyone how many hands each person shook that night. To his surprise, he received a unique answer from everyone. How many hands did Alice shake that night?"

Note: 

- Couples did not share a handshake since they already know each other. 

- A person cannot shake hands with themselves. 

 I had a different equation originally for this solution and I will include it as well if you are struggling with this problem. 

Find the x coordinate of the intersection of these two lines:

(Edit: I somehow deleted my equation and I have now forgotten it. RIP looks liek you'll have to do the hard one) 

Both of these questions should solve for the same value. You should only include the value in your code once.

Please keep answers to yourself. If you would like to confirm your answer feel free to message me personally 8)

Good luck solving these equations  

And yes, here's your joke:

Today at the bank, an old lady asked me to help check her balance. So I pushed her over.