(3x-6)(x-6)=420

Solution for (3x-6)(x-6)=420 equation:

(3x-6)(x-6)=420

We move all terms to the left:

(3x-6)(x-6)-(420)=0

We multiply parentheses ..

(+3x^2-18x-6x+36)-420=0

We get rid of parentheses

3x^2-18x-6x+36-420=0

We add all the numbers together, and all the variables

3x^2-24x-384=0

a = 3; b = -24; c = -384;
Δ = b2-4ac
Δ = -242-4·3·(-384)
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-72}{2*3}=\frac{-48}{6}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+72}{2*3}=\frac{96}{6}
=16
$