3x(4x-8)=-24+12x

Solution for 3x(4x-8)=-24+12x equation:

3x(4x-8)=-24+12x

We move all terms to the left:

3x(4x-8)-(-24+12x)=0

We add all the numbers together, and all the variables

3x(4x-8)-(12x-24)=0

We multiply parentheses

12x^2-24x-(12x-24)=0

We get rid of parentheses

12x^2-24x-12x+24=0

We add all the numbers together, and all the variables

12x^2-36x+24=0

a = 12; b = -36; c = +24;
Δ = b2-4ac
Δ = -362-4·12·24
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{-(-36)-12}{2*12}=\frac{24}{24}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+12}{2*12}=\frac{48}{24}
=2
$