-2n-4(8n+5)n=2

Solution for -2n-4(8n+5)n=2 equation:

-2n-4(8n+5)n=2

We move all terms to the left:

-2n-4(8n+5)n-(2)=0

We multiply parentheses

-32n^2-2n-20n-2=0

We add all the numbers together, and all the variables

-32n^2-22n-2=0

a = -32; b = -22; c = -2;
Δ = b2-4ac
Δ = -222-4·(-32)·(-2)
Δ = 228
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:

$\sqrt{\Delta}=\sqrt{228}=\sqrt{4*57}=\sqrt{4}*\sqrt{57}=2\sqrt{57}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{57}}{2*-32}=\frac{22-2\sqrt{57}}{-64}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{57}}{2*-32}=\frac{22+2\sqrt{57}}{-64}
$