3n^2-16=-8n

Solution for 3n^2-16=-8n equation:

3n^2-16=-8n

We move all terms to the left:

3n^2-16-(-8n)=0

We get rid of parentheses

3n^2+8n-16=0

a = 3; b = 8; c = -16;
Δ = b2-4ac
Δ = 82-4·3·(-16)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-16}{2*3}=\frac{-24}{6}
=-4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+16}{2*3}=\frac{8}{6}
=1+1/3
$