How to introduce polyamory to my relationship

I have been dating my boyfriend for 7 years. I love him, and don't want to lose him, but I met another man who became very important to me and we feel madly in love with each other. Now, I don't want to lose either of them. That's why I am considering a poly relationship. The new man agreed. I still haven't asked my boyfriend yet, because I'm scared I'll shock him. 

Is there anybody out there who lives in a poly relationship? Do you have any tips how to start the topic with my boyfriend? I'm also interested in your stories - how did you meet the third one, how are you coping with common problems (sharing time, jealousy, etc.)

Thank you for reading this!