(a-4)(a-2)=2

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

(a-4)(a-2)=2

We move all terms to the left:

(a-4)(a-2)-(2)=0

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

a^2-6a+6=0

a = 1; b = -6; c = +6;
Δ = b2-4ac
Δ = -62-4·1·6
Δ = 12
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{3}}{2*1}=\frac{6-2\sqrt{3}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{3}}{2*1}=\frac{6+2\sqrt{3}}{2}
$