616=5n^2+n

Solution for 616=5n^2+n equation:

616=5n^2+n

We move all terms to the left:

616-(5n^2+n)=0

We get rid of parentheses

-5n^2-n+616=0

We add all the numbers together, and all the variables

-5n^2-1n+616=0

a = -5; b = -1; c = +616;
Δ = b2-4ac
Δ = -12-4·(-5)·616
Δ = 12321
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12321}=111$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-111}{2*-5}=\frac{-110}{-10}
=+11
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+111}{2*-5}=\frac{112}{-10}
=-11+1/5
$