180=4n+8n2-8

Solution for 180=4n+8n2-8 equation:

180=4n+8n^2-8

We move all terms to the left:

180-(4n+8n^2-8)=0

We get rid of parentheses

-8n^2-4n+8+180=0

We add all the numbers together, and all the variables

-8n^2-4n+188=0

a = -8; b = -4; c = +188;
Δ = b2-4ac
Δ = -42-4·(-8)·188
Δ = 6032
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:

$\sqrt{\Delta}=\sqrt{6032}=\sqrt{16*377}=\sqrt{16}*\sqrt{377}=4\sqrt{377}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{377}}{2*-8}=\frac{4-4\sqrt{377}}{-16}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{377}}{2*-8}=\frac{4+4\sqrt{377}}{-16}
$