n(n+6)=520

Solution for n(n+6)=520 equation:

n(n+6)=520

We move all terms to the left:

n(n+6)-(520)=0

We multiply parentheses

n^2+6n-520=0

a = 1; b = 6; c = -520;
Δ = b2-4ac
Δ = 62-4·1·(-520)
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-46}{2*1}=\frac{-52}{2}
=-26
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+46}{2*1}=\frac{40}{2}
=20
$