-3n(n+8)-4=-40-n

Solution for -3n(n+8)-4=-40-n equation:

-3n(n+8)-4=-40-n

We move all terms to the left:

-3n(n+8)-4-(-40-n)=0

We add all the numbers together, and all the variables

-3n(n+8)-(-1n-40)-4=0

We multiply parentheses

-3n^2-24n-(-1n-40)-4=0

We get rid of parentheses

-3n^2-24n+1n+40-4=0

We add all the numbers together, and all the variables

-3n^2-23n+36=0

a = -3; b = -23; c = +36;
Δ = b2-4ac
Δ = -232-4·(-3)·36
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-31}{2*-3}=\frac{-8}{-6}
=1+1/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+31}{2*-3}=\frac{54}{-6}
=-9
$