3(x-2)(x-2)-6=0

Solution for 3(x-2)(x-2)-6=0 equation:

3(x-2)(x-2)-6=0

We multiply parentheses ..

3(+x^2-2x-2x+4)-6=0

We multiply parentheses

3x^2-6x-6x+12-6=0

We add all the numbers together, and all the variables

3x^2-12x+6=0

a = 3; b = -12; c = +6;
Δ = b2-4ac
Δ = -122-4·3·6
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{2}}{2*3}=\frac{12-6\sqrt{2}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{2}}{2*3}=\frac{12+6\sqrt{2}}{6}
$