18n+80=n^2

Solution for 18n+80=n^2 equation:

18n+80=n^2

We move all terms to the left:

18n+80-(n^2)=0

determiningTheFunctionDomain
-n^2+18n+80=0

We add all the numbers together, and all the variables

-1n^2+18n+80=0

a = -1; b = 18; c = +80;
Δ = b2-4ac
Δ = 182-4·(-1)·80
Δ = 644
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{644}=\sqrt{4*161}=\sqrt{4}*\sqrt{161}=2\sqrt{161}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{161}}{2*-1}=\frac{-18-2\sqrt{161}}{-2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{161}}{2*-1}=\frac{-18+2\sqrt{161}}{-2}
$