(n-4)12n=6

Solution for (n-4)12n=6 equation:

(n-4)12n=6

We move all terms to the left:

(n-4)12n-(6)=0

We multiply parentheses

12n^2-48n-6=0

a = 12; b = -48; c = -6;
Δ = b2-4ac
Δ = -482-4·12·(-6)
Δ = 2592
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:

$\sqrt{\Delta}=\sqrt{2592}=\sqrt{1296*2}=\sqrt{1296}*\sqrt{2}=36\sqrt{2}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-36\sqrt{2}}{2*12}=\frac{48-36\sqrt{2}}{24}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+36\sqrt{2}}{2*12}=\frac{48+36\sqrt{2}}{24}
$