(x-2)(x-4)=2x

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

(x-2)(x-4)=2x

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+x^2-4x-2x+8)-2x=0

We get rid of parentheses

x^2-4x-2x-2x+8=0

We add all the numbers together, and all the variables

x^2-8x+8=0

a = 1; b = -8; c = +8;
Δ = b2-4ac
Δ = -82-4·1·8
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{2}}{2*1}=\frac{8-4\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{2}}{2*1}=\frac{8+4\sqrt{2}}{2}
$