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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2-4x-92=0

a = 1; b = -4; c = -92;
Δ = b2-4ac
Δ = -42-4·1·(-92)
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-8\sqrt{6}}{2*1}=\frac{4-8\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8\sqrt{6}}{2*1}=\frac{4+8\sqrt{6}}{2}
$