112-180n=-28n^2

Solution for 112-180n=-28n^2 equation:

112-180n=-28n^2

We move all terms to the left:

112-180n-(-28n^2)=0

We get rid of parentheses

28n^2-180n+112=0

a = 28; b = -180; c = +112;
Δ = b2-4ac
Δ = -1802-4·28·112
Δ = 19856
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:

$\sqrt{\Delta}=\sqrt{19856}=\sqrt{16*1241}=\sqrt{16}*\sqrt{1241}=4\sqrt{1241}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-4\sqrt{1241}}{2*28}=\frac{180-4\sqrt{1241}}{56}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+4\sqrt{1241}}{2*28}=\frac{180+4\sqrt{1241}}{56}
$