The elo system.

So, I had started playing league back in season two when force of nature was a thing. Now it took me a while to convenience myself that I even wanted to play ranked seriously, I believe I never finished provisional once before season four. When I did complete them I was like "yea, ranked whooo, ranked bronze five but still whoo I'm on the board some where, but I'm not playing it again". Towards the end of season four I picked it back up again and started to play seriously in the time I had between school and other things. I manged to claw my way up two tiers to bronze three. Not very far on the ladder but enough along that I felt like I accomplished something before the season ended. Then came provisionals again. Pumped to give it my all and hopefully be placed if not out of bronze at least a tier or two higher. Winning seven out of ten of them I thought my self to be in pretty good shape, that is until the client pooped back up again after my last game. Not only did I not go up in tier I went back down.... to bronze five again. I'm at the moment extremely disheartened and discouraged. I put all I had to give into it, I'm also often times the positive guy on the team that rallies every one not to give up, stay focused and to say that being at each others throats ain't going to help us, but apparently it wasn't enough and was also bad enough to drop me back down two tiers. I'm sitting here in dismay and confusion on how is it riot that the elo system actual works. How its calculated. I'm not looking for a simple answer, I''m looking for actual equations on how this is calculated. At the moment I understand that the ladder is long and the set back I have experienced is small compared to the whole. However it was something that I took some pride in getting that far. Having to valiantly press on pass each loss, not want to scream in frustration at every AFK person that was at one point on my team, not dodge and believe that a support might work and even though in then end it doesn't or having too sit and try to rally the team and coach a bit and suggest that people not wander when we need to defend or say that we need to shove a lane now, and have them all not listen and continue to not communicate or say that they'll do what they want. Am I saying that I'm not to blame for some of my losses, of course not. There has been plenty of times that I'll make a mistake and I will get upset about it. However I take this and try to learn form it (most of the time). What was I doing wrong, how could of that gone better. I also know that I can't cs worth my life. So I am not just another guy bitching about how he is stuck in "elo hell" because truth be told, I can solidly say that with enough time and determination, any one can get out of bronze. My problem here is I just feel like this elo system to individual stand point is not fair. I just want to know what goes into the programmed discussion making to put me back in bronze five even though I did better this provisional then my first. I give it my all and it gets kicked right back in my face along with an unnecessary punch to the stomach. Like ouch, riot.