(x-6)*(-12+2*x)=3024

Solution for (x-6)*(-12+2*x)=3024 equation:

(x-6)(-12+2x)=3024

We move all terms to the left:

(x-6)(-12+2x)-(3024)=0

We add all the numbers together, and all the variables

(x-6)(2x-12)-3024=0

We multiply parentheses ..

(+2x^2-12x-12x+72)-3024=0

We get rid of parentheses

2x^2-12x-12x+72-3024=0

We add all the numbers together, and all the variables

2x^2-24x-2952=0

a = 2; b = -24; c = -2952;
Δ = b2-4ac
Δ = -242-4·2·(-2952)
Δ = 24192
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:

$\sqrt{\Delta}=\sqrt{24192}=\sqrt{576*42}=\sqrt{576}*\sqrt{42}=24\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-24\sqrt{42}}{2*2}=\frac{24-24\sqrt{42}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+24\sqrt{42}}{2*2}=\frac{24+24\sqrt{42}}{4}
$