3.x(2x-4)=6x-12

Solution for 3.x(2x-4)=6x-12 equation:

3.x(2x-4)=6x-12

We move all terms to the left:

3.x(2x-4)-(6x-12)=0

We multiply parentheses

6x^2-12x-(6x-12)=0

We get rid of parentheses

6x^2-12x-6x+12=0

We add all the numbers together, and all the variables

6x^2-18x+12=0

a = 6; b = -18; c = +12;
Δ = b2-4ac
Δ = -182-4·6·12
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6}{2*6}=\frac{12}{12}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6}{2*6}=\frac{24}{12}
=2
$