-40+2n=4n-8n(n+8)

Solution for -40+2n=4n-8n(n+8) equation:

-40+2n=4n-8n(n+8)

We move all terms to the left:

-40+2n-(4n-8n(n+8))=0


We calculate terms in parentheses: -(4n-8n(n+8)), so:

4n-8n(n+8)

We multiply parentheses

-8n^2+4n-64n

We add all the numbers together, and all the variables

-8n^2-60n

Back to the equation:

-(-8n^2-60n)


We get rid of parentheses

8n^2+60n+2n-40=0

We add all the numbers together, and all the variables

8n^2+62n-40=0

a = 8; b = 62; c = -40;
Δ = b2-4ac
Δ = 622-4·8·(-40)
Δ = 5124
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:

$\sqrt{\Delta}=\sqrt{5124}=\sqrt{4*1281}=\sqrt{4}*\sqrt{1281}=2\sqrt{1281}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(62)-2\sqrt{1281}}{2*8}=\frac{-62-2\sqrt{1281}}{16}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(62)+2\sqrt{1281}}{2*8}=\frac{-62+2\sqrt{1281}}{16}
$