(n+8)(8n+1)=0

Solution for (n+8)(8n+1)=0 equation:

(n+8)(8n+1)=0

We multiply parentheses ..

(+8n^2+n+64n+8)=0

We get rid of parentheses

8n^2+n+64n+8=0

We add all the numbers together, and all the variables

8n^2+65n+8=0

a = 8; b = 65; c = +8;
Δ = b2-4ac
Δ = 652-4·8·8
Δ = 3969
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3969}=63$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(65)-63}{2*8}=\frac{-128}{16}
=-8
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(65)+63}{2*8}=\frac{-2}{16}
=-1/8
$