0.08n+0.12n(n+500)=180

Solution for 0.08n+0.12n(n+500)=180 equation:

0.08n+0.12n(n+500)=180

We move all terms to the left:

0.08n+0.12n(n+500)-(180)=0

We multiply parentheses

0n^2+0.08n+0n-180=0

We add all the numbers together, and all the variables

n^2+1.08n-180=0

a = 1; b = 1.08; c = -180;
Δ = b2-4ac
Δ = 1.082-4·1·(-180)
Δ = 721.1664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1.08)-\sqrt{721.1664}}{2*1}=\frac{-1.08-\sqrt{721.1664}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1.08)+\sqrt{721.1664}}{2*1}=\frac{-1.08+\sqrt{721.1664}}{2}
$