3(x-6)(2.7x-6)=600

Solution for 3(x-6)(2.7x-6)=600 equation:

3(x-6)(2.7x-6)=600

We move all terms to the left:

3(x-6)(2.7x-6)-(600)=0

We multiply parentheses ..

3(+2x^2-6x-12x+36)-600=0

We multiply parentheses

6x^2-18x-36x+108-600=0

We add all the numbers together, and all the variables

6x^2-54x-492=0

a = 6; b = -54; c = -492;
Δ = b2-4ac
Δ = -542-4·6·(-492)
Δ = 14724
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:

$\sqrt{\Delta}=\sqrt{14724}=\sqrt{36*409}=\sqrt{36}*\sqrt{409}=6\sqrt{409}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-6\sqrt{409}}{2*6}=\frac{54-6\sqrt{409}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+6\sqrt{409}}{2*6}=\frac{54+6\sqrt{409}}{12}
$