In a hockey championship, there are 153 matches played. Every two team played one match with each other. The number of teams participating in the championship is:

There are 153 matches to be played with let;s assume n teams.
Therefore the number of matches that can be played with these n teams is:
( 1 + 2 + 3 + . . . + n - 1 )
Σ ( n - 1 ) = 153
Σ ( n ) - Σ ( 1 ) = 153
( n ( n- 1 ) ) / 2 - n = 153
n ^ 2 - n = 153 * 2
n ^ 2 - n - 306
n ^ 2 - 18 * n + 17 * n - 306 = 0
n( n - 18 ) + 17( n - 18) = 0
(n - 18)( n + 17 ) = 0
n = 18 because there cannot be -ve teams.

(I based logic first using 5 teams and found the number of matches possible and turns out it was the right logic, so future questions like these you can use this method to arrive at the right answer!)

total number of matches = nC2
=> nC2 = 153


n(n-1)/2! = 153

n(n-1) = 2 × 153 = 306
-306 + 1 = -305
-153 + 2 = -151
-102 + 3 = -99
-51 + 6 = -45
-34 + 9 = -25
-18 + 17 = -1
-17 + 18 = 1

n2 + 17n - 18n - 306 =0
for n =18, n(n-1) = 18 × 17 = 306
i.e., total number of games = 18