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So basic idea is right. But you’ve got problem when you computing that formula.
First, you say, that beehive with 7, 8, 9 cells are valid. For 7 it’s correct, but not for others.
This is caused in line
long hold=n/3;
You want to use double variable, because you use integer division.
Second mistake, when you divide by some number and want double result, you must divide by double. And number 3 is not double but integer. But 3.0 is double.
So correct code should looks like:
double hold=n/3.0;
double ans=(Math.sqrt(1+4*hold)-1)/2.0;
Now you will be rewarded by Accepted 
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made the corrections,got AC! thanks a lot! 
but couldn’t understand what you meant by this line: “you say, that beehive with 7, 8, 9 cells are valid.”
i don’t understand how the previous line (long hold=n/3;) accepted 8 and 9 as valid numbers. Could you please elaborate?
Well. Take n=7. You substract 1 and hold=6/3=2. Than you compute (sqrt(1+4*hold)-1)/2 and get ans=1. But when you’ve got n=8, than hold=7/3 but that is still 2, because you using integer not double arithmetic. So you again get ans=1. Similary with n=9. And when you’ve got n=10, than hold=9/3=3 and ans=1,302775638 what not integer number and you correctly say ‘N’. Do you understand now?
Main difference a/b with integer numbers is floor(a/b) with doubles.
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yes now got it! thanks for the explanation