8n-2n(n+5)=3+6n

Solution for 8n-2n(n+5)=3+6n equation:

8n-2n(n+5)=3+6n

We move all terms to the left:

8n-2n(n+5)-(3+6n)=0

We add all the numbers together, and all the variables

8n-2n(n+5)-(6n+3)=0

We multiply parentheses

-2n^2+8n-10n-(6n+3)=0

We get rid of parentheses

-2n^2+8n-10n-6n-3=0

We add all the numbers together, and all the variables

-2n^2-8n-3=0

a = -2; b = -8; c = -3;
Δ = b2-4ac
Δ = -82-4·(-2)·(-3)
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{10}}{2*-2}=\frac{8-2\sqrt{10}}{-4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{10}}{2*-2}=\frac{8+2\sqrt{10}}{-4}
$