2n^2-4n=16

Solution for 2n^2-4n=16 equation:

2n^2-4n=16

We move all terms to the left:

2n^2-4n-(16)=0

a = 2; b = -4; c = -16;
Δ = b2-4ac
Δ = -42-4·2·(-16)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-12}{2*2}=\frac{-8}{4}
=-2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+12}{2*2}=\frac{16}{4}
=4
$