(2x-2)*(x-2)=96

Solution for (2x-2)*(x-2)=96 equation:

(2x-2)(x-2)=96

We move all terms to the left:

(2x-2)(x-2)-(96)=0

We multiply parentheses ..

(+2x^2-4x-2x+4)-96=0

We get rid of parentheses

2x^2-4x-2x+4-96=0

We add all the numbers together, and all the variables

2x^2-6x-92=0

a = 2; b = -6; c = -92;
Δ = b2-4ac
Δ = -62-4·2·(-92)
Δ = 772
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:

$\sqrt{\Delta}=\sqrt{772}=\sqrt{4*193}=\sqrt{4}*\sqrt{193}=2\sqrt{193}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{193}}{2*2}=\frac{6-2\sqrt{193}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{193}}{2*2}=\frac{6+2\sqrt{193}}{4}
$