2x(6x-6)=4(3x-2)

Solution for 2x(6x-6)=4(3x-2) equation:

2x(6x-6)=4(3x-2)

We move all terms to the left:

2x(6x-6)-(4(3x-2))=0

We multiply parentheses

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


We calculate terms in parentheses: -(4(3x-2)), so:

4(3x-2)

We multiply parentheses

12x-8

Back to the equation:

-(12x-8)


We get rid of parentheses

12x^2-12x-12x+8=0

We add all the numbers together, and all the variables

12x^2-24x+8=0

a = 12; b = -24; c = +8;
Δ = b2-4ac
Δ = -242-4·12·8
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-8\sqrt{3}}{2*12}=\frac{24-8\sqrt{3}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+8\sqrt{3}}{2*12}=\frac{24+8\sqrt{3}}{24}
$