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

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

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

We move all terms to the left:

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

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2-16x+4=0

a = 2; b = -16; c = +4;
Δ = b2-4ac
Δ = -162-4·2·4
Δ = 224
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:

$\sqrt{\Delta}=\sqrt{224}=\sqrt{16*14}=\sqrt{16}*\sqrt{14}=4\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{14}}{2*2}=\frac{16-4\sqrt{14}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{14}}{2*2}=\frac{16+4\sqrt{14}}{4}
$