I just can't increase my elo. I win a game i get +13 points, next game i lose and lose -13 points. Its just endless circle. I got 1117 Solo queue ELO with 53W-52L. How do i increase it?

Win more than you loose, kinda obvious though?
-.-

Break the circle, win two in a row.

I've wondered too, but after reading some threads I came to conclusion that the best way to get to mid-high elo (where I believe I belong) is start a new account, master some champions and use them in duo queue with your friend and start your new ranked from winning.

How to increase ELO practically: Pick a champion and master it, you will gain elo eventually.
How to increase ELO theoretically: In order to gain elo, you must have higher than 50% win rate at the present. This means that if you win 100 games in a row and after that your win-loss rating goes to 50-50%, you cannot gain elo. This is also true in the other side of the spectrum; if you were 1800, lost 20 games, then go to win 50-50, you cannot get back to 1800.

Just to give my situation as an example:

173 wins - 137 losses - elo rating 1837.
Win rate: 56.2%

But what abut those who got like +10 win/lose ratio ranked games and had 1504 ratin' and then got 8 games 4 feeders ? i admit i failed few times -.-

What you ask is : How to win more elo than you lose?
Be extra lucky!

Not true. LLN (law of large numbers) favors always skill over luck as a factor.