3(x-4)(x-4)=27

Solution for 3(x-4)(x-4)=27 equation:

3(x-4)(x-4)=27

We move all terms to the left:

3(x-4)(x-4)-(27)=0

We multiply parentheses ..

3(+x^2-4x-4x+16)-27=0

We multiply parentheses

3x^2-12x-12x+48-27=0

We add all the numbers together, and all the variables

3x^2-24x+21=0

a = 3; b = -24; c = +21;
Δ = b2-4ac
Δ = -242-4·3·21
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-18}{2*3}=\frac{6}{6}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+18}{2*3}=\frac{42}{6}
=7
$