X(x-2)=4x-2

Solution for X(x-2)=4x-2 equation:

X(X-2)=4X-2

We move all terms to the left:

X(X-2)-(4X-2)=0

We multiply parentheses

X^2-2X-(4X-2)=0

We get rid of parentheses

X^2-2X-4X+2=0

We add all the numbers together, and all the variables

X^2-6X+2=0

a = 1; b = -6; c = +2;
Δ = b2-4ac
Δ = -62-4·1·2
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{7}}{2*1}=\frac{6-2\sqrt{7}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{7}}{2*1}=\frac{6+2\sqrt{7}}{2}
$