12x(4-x)3=6x-2

Solution for 12x(4-x)3=6x-2 equation:

12x(4-x)3=6x-2

We move all terms to the left:

12x(4-x)3-(6x-2)=0

We add all the numbers together, and all the variables

12x(-1x+4)3-(6x-2)=0

We multiply parentheses

-36x^2+144x-(6x-2)=0

We get rid of parentheses

-36x^2+144x-6x+2=0

We add all the numbers together, and all the variables

-36x^2+138x+2=0

a = -36; b = 138; c = +2;
Δ = b2-4ac
Δ = 1382-4·(-36)·2
Δ = 19332
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:

$\sqrt{\Delta}=\sqrt{19332}=\sqrt{36*537}=\sqrt{36}*\sqrt{537}=6\sqrt{537}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(138)-6\sqrt{537}}{2*-36}=\frac{-138-6\sqrt{537}}{-72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(138)+6\sqrt{537}}{2*-36}=\frac{-138+6\sqrt{537}}{-72}
$