-8n(n+4)+34=-4n-10

Solution for -8n(n+4)+34=-4n-10 equation:

-8n(n+4)+34=-4n-10

We move all terms to the left:

-8n(n+4)+34-(-4n-10)=0

We multiply parentheses

-8n^2-32n-(-4n-10)+34=0

We get rid of parentheses

-8n^2-32n+4n+10+34=0

We add all the numbers together, and all the variables

-8n^2-28n+44=0

a = -8; b = -28; c = +44;
Δ = b2-4ac
Δ = -282-4·(-8)·44
Δ = 2192
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:

$\sqrt{\Delta}=\sqrt{2192}=\sqrt{16*137}=\sqrt{16}*\sqrt{137}=4\sqrt{137}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{137}}{2*-8}=\frac{28-4\sqrt{137}}{-16}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{137}}{2*-8}=\frac{28+4\sqrt{137}}{-16}
$