-4(2n-6)n+6=0

Solution for -4(2n-6)n+6=0 equation:

-4(2n-6)n+6=0

We multiply parentheses

-8n^2+24n+6=0

a = -8; b = 24; c = +6;
Δ = b2-4ac
Δ = 242-4·(-8)·6
Δ = 768
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:

$\sqrt{\Delta}=\sqrt{768}=\sqrt{256*3}=\sqrt{256}*\sqrt{3}=16\sqrt{3}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-16\sqrt{3}}{2*-8}=\frac{-24-16\sqrt{3}}{-16}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+16\sqrt{3}}{2*-8}=\frac{-24+16\sqrt{3}}{-16}
$