(180n-360)n=140

Solution for (180n-360)n=140 equation:

(180n-360)n=140

We move all terms to the left:

(180n-360)n-(140)=0

We multiply parentheses

180n^2-360n-140=0

a = 180; b = -360; c = -140;
Δ = b2-4ac
Δ = -3602-4·180·(-140)
Δ = 230400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{230400}=480$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-480}{2*180}=\frac{-120}{360}
=-1/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+480}{2*180}=\frac{840}{360}
=2+1/3
$