8n^2-64=-16n

Solution for 8n^2-64=-16n equation:

8n^2-64=-16n

We move all terms to the left:

8n^2-64-(-16n)=0

We get rid of parentheses

8n^2+16n-64=0

a = 8; b = 16; c = -64;
Δ = b2-4ac
Δ = 162-4·8·(-64)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-48}{2*8}=\frac{-64}{16}
=-4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+48}{2*8}=\frac{32}{16}
=2
$