6n^2=12n-4

Solution for 6n^2=12n-4 equation:

6n^2=12n-4

We move all terms to the left:

6n^2-(12n-4)=0

We get rid of parentheses

6n^2-12n+4=0

a = 6; b = -12; c = +4;
Δ = b2-4ac
Δ = -122-4·6·4
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{3}}{2*6}=\frac{12-4\sqrt{3}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{3}}{2*6}=\frac{12+4\sqrt{3}}{12}
$