4n(40+n)=180

Solution for 4n(40+n)=180 equation:

4n(40+n)=180

We move all terms to the left:

4n(40+n)-(180)=0

We add all the numbers together, and all the variables

4n(n+40)-180=0

We multiply parentheses

4n^2+160n-180=0

a = 4; b = 160; c = -180;
Δ = b2-4ac
Δ = 1602-4·4·(-180)
Δ = 28480
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:

$\sqrt{\Delta}=\sqrt{28480}=\sqrt{64*445}=\sqrt{64}*\sqrt{445}=8\sqrt{445}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(160)-8\sqrt{445}}{2*4}=\frac{-160-8\sqrt{445}}{8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(160)+8\sqrt{445}}{2*4}=\frac{-160+8\sqrt{445}}{8}
$