(X-2)(x-6)=2x

Solution for (X-2)(x-6)=2x equation:

(X-2)(X-6)=2X

We move all terms to the left:

(X-2)(X-6)-(2X)=0

We add all the numbers together, and all the variables

-2X+(X-2)(X-6)=0

We multiply parentheses ..

(+X^2-6X-2X+12)-2X=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

X^2-10X+12=0

a = 1; b = -10; c = +12;
Δ = b2-4ac
Δ = -102-4·1·12
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{13}}{2*1}=\frac{10-2\sqrt{13}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{13}}{2*1}=\frac{10+2\sqrt{13}}{2}
$