-8n(n+5)=-5(8+6n)

Solution for -8n(n+5)=-5(8+6n) equation:

-8n(n+5)=-5(8+6n)

We move all terms to the left:

-8n(n+5)-(-5(8+6n))=0

We add all the numbers together, and all the variables

-8n(n+5)-(-5(6n+8))=0

We multiply parentheses

-8n^2-40n-(-5(6n+8))=0


We calculate terms in parentheses: -(-5(6n+8)), so:

-5(6n+8)

We multiply parentheses

-30n-40

Back to the equation:

-(-30n-40)


We get rid of parentheses

-8n^2-40n+30n+40=0

We add all the numbers together, and all the variables

-8n^2-10n+40=0

a = -8; b = -10; c = +40;
Δ = b2-4ac
Δ = -102-4·(-8)·40
Δ = 1380
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:

$\sqrt{\Delta}=\sqrt{1380}=\sqrt{4*345}=\sqrt{4}*\sqrt{345}=2\sqrt{345}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{345}}{2*-8}=\frac{10-2\sqrt{345}}{-16}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{345}}{2*-8}=\frac{10+2\sqrt{345}}{-16}
$