3(x-2)(x-2)=48

Solution for 3(x-2)(x-2)=48 equation:

3(x-2)(x-2)=48

We move all terms to the left:

3(x-2)(x-2)-(48)=0

We multiply parentheses ..

3(+x^2-2x-2x+4)-48=0

We multiply parentheses

3x^2-6x-6x+12-48=0

We add all the numbers together, and all the variables

3x^2-12x-36=0

a = 3; b = -12; c = -36;
Δ = b2-4ac
Δ = -122-4·3·(-36)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-24}{2*3}=\frac{-12}{6}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+24}{2*3}=\frac{36}{6}
=6
$