For example:

```
public int arrangeCoins(int n) {
return (int) (-1.0 + Math.sqrt((8L * n) + 1)) >> 1;
}
```

Explain:

using the formule of delta,

x= (-b(+-)sqrt(b^2 - 4ac) ) / 2a

as we know,the sequence of number is regular like:

an-an-1 = n-1;

an-1 - an-2 = n-2;

an-2 - an-3 = n-3;

.

.

.

.

a3 - a2 = 2;

a2-a1 = 1;

so,we can accumulate above sequences,then

an-a1 = (1+2+3+....+n-1)

simplify

an = (n^2-n) /2 + a1 ,and a1 = 1 (the head of the sequence for each row,and we define the head as an0,tail is ann)

so

ann = an0 + n-1 = (n^2-n)/2 + n;

simplify

X = (n^2-n)/2 + n

double

2X = n^2-n + 2n,

so,

n^2+n-2X = 0;

so we can use the formule of delta:

x= (-b(+-)sqrt(b^2 - 4ac) ) / 2a

that is the result for the problem