12n+n2+(n+20)=180

Solution for 12n+n2+(n+20)=180 equation:

12n+n2+(n+20)=180

We move all terms to the left:

12n+n2+(n+20)-(180)=0

We add all the numbers together, and all the variables

n^2+12n+(n+20)-180=0

We get rid of parentheses

n^2+12n+n+20-180=0

We add all the numbers together, and all the variables

n^2+13n-160=0

a = 1; b = 13; c = -160;
Δ = b2-4ac
Δ = 132-4·1·(-160)
Δ = 809
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{-(13)-\sqrt{809}}{2*1}=\frac{-13-\sqrt{809}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{809}}{2*1}=\frac{-13+\sqrt{809}}{2}
$