2(x-2)(x-4)=132

Solution for 2(x-2)(x-4)=132 equation:

2(x-2)(x-4)=132

We move all terms to the left:

2(x-2)(x-4)-(132)=0

We multiply parentheses ..

2(+x^2-4x-2x+8)-132=0

We multiply parentheses

2x^2-8x-4x+16-132=0

We add all the numbers together, and all the variables

2x^2-12x-116=0

a = 2; b = -12; c = -116;
Δ = b2-4ac
Δ = -122-4·2·(-116)
Δ = 1072
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:

$\sqrt{\Delta}=\sqrt{1072}=\sqrt{16*67}=\sqrt{16}*\sqrt{67}=4\sqrt{67}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{67}}{2*2}=\frac{12-4\sqrt{67}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{67}}{2*2}=\frac{12+4\sqrt{67}}{4}
$