Sum of first k natural number is given by:

k(k+1)/2

to find k we need to solve the equation, where sum = n

we need to find positive root of the equation:

k-sq + k - 2n = 0

which is given by = (-b + sqrt(b-sq - 4ac))/2a

```
public class Solution {
public int arrangeCoins(int n) {
if (n == 0) {
return 0;
}
int b = 1;
int a = 1;
long c = -n*2l;
int res = (int) (-b + Math.sqrt(b*b - 4*a*c))/2*a;
return res;
}
}
```