3n^2-8n=16

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

3n^2-8n=16

We move all terms to the left:

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