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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

4x-x(-3x+4)-12=0

We multiply parentheses

3x^2+4x-4x-12=0

We add all the numbers together, and all the variables

3x^2-12=0

a = 3; b = 0; c = -12;
Δ = b2-4ac
Δ = 02-4·3·(-12)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12}{2*3}=\frac{-12}{6}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12}{2*3}=\frac{12}{6}
=2
$