6-8n=2n^2

Solution for 6-8n=2n^2 equation:

6-8n=2n^2

We move all terms to the left:

6-8n-(2n^2)=0

determiningTheFunctionDomain
-2n^2-8n+6=0

a = -2; b = -8; c = +6;
Δ = b2-4ac
Δ = -82-4·(-2)·6
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{7}}{2*-2}=\frac{8-4\sqrt{7}}{-4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{7}}{2*-2}=\frac{8+4\sqrt{7}}{-4}
$