-8n(n+3)=-36-4n

Solution for -8n(n+3)=-36-4n equation:

-8n(n+3)=-36-4n

We move all terms to the left:

-8n(n+3)-(-36-4n)=0

We add all the numbers together, and all the variables

-8n(n+3)-(-4n-36)=0

We multiply parentheses

-8n^2-24n-(-4n-36)=0

We get rid of parentheses

-8n^2-24n+4n+36=0

We add all the numbers together, and all the variables

-8n^2-20n+36=0

a = -8; b = -20; c = +36;
Δ = b2-4ac
Δ = -202-4·(-8)·36
Δ = 1552
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:

$\sqrt{\Delta}=\sqrt{1552}=\sqrt{16*97}=\sqrt{16}*\sqrt{97}=4\sqrt{97}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{97}}{2*-8}=\frac{20-4\sqrt{97}}{-16}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{97}}{2*-8}=\frac{20+4\sqrt{97}}{-16}
$