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

Solution for 2(x-6)(6-3x)=0 equation:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We multiply parentheses

-6x^2+12x+36x-72=0

We add all the numbers together, and all the variables

-6x^2+48x-72=0

a = -6; b = 48; c = -72;
Δ = b2-4ac
Δ = 482-4·(-6)·(-72)
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{-(48)-24}{2*-6}=\frac{-72}{-12}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+24}{2*-6}=\frac{-24}{-12}
=+2
$