3x^2=12x-4

Solution for 3x^2=12x-4 equation:

3x^2=12x-4

We move all terms to the left:

3x^2-(12x-4)=0

We get rid of parentheses

3x^2-12x+4=0

a = 3; b = -12; c = +4;
Δ = b2-4ac
Δ = -122-4·3·4
Δ = 96
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{6}}{2*3}=\frac{12-4\sqrt{6}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{6}}{2*3}=\frac{12+4\sqrt{6}}{6}
$