3(2x-6)(x-6)=324

Solution for 3(2x-6)(x-6)=324 equation:

3(2x-6)(x-6)=324

We move all terms to the left:

3(2x-6)(x-6)-(324)=0

We multiply parentheses ..

3(+2x^2-12x-6x+36)-324=0

We multiply parentheses

6x^2-36x-18x+108-324=0

We add all the numbers together, and all the variables

6x^2-54x-216=0

a = 6; b = -54; c = -216;
Δ = b2-4ac
Δ = -542-4·6·(-216)
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-90}{2*6}=\frac{-36}{12}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+90}{2*6}=\frac{144}{12}
=12
$