(y-4)(y-2)=4

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

(y-4)(y-2)=4

We move all terms to the left:

(y-4)(y-2)-(4)=0

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

y^2-6y+4=0

a = 1; b = -6; c = +4;
Δ = b2-4ac
Δ = -62-4·1·4
Δ = 20
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{5}}{2*1}=\frac{6-2\sqrt{5}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{5}}{2*1}=\frac{6+2\sqrt{5}}{2}
$