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

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

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

We move all terms to the left:

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

We multiply parentheses

2x^2-12x-(4x-4)+6=0

We get rid of parentheses

2x^2-12x-4x+4+6=0

We add all the numbers together, and all the variables

2x^2-16x+10=0

a = 2; b = -16; c = +10;
Δ = b2-4ac
Δ = -162-4·2·10
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{11}}{2*2}=\frac{16-4\sqrt{11}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{11}}{2*2}=\frac{16+4\sqrt{11}}{4}
$