2x(6x-12)=3(4x-8)

Solution for 2x(6x-12)=3(4x-8) equation:

2x(6x-12)=3(4x-8)

We move all terms to the left:

2x(6x-12)-(3(4x-8))=0

We multiply parentheses

12x^2-24x-(3(4x-8))=0


We calculate terms in parentheses: -(3(4x-8)), so:

3(4x-8)

We multiply parentheses

12x-24

Back to the equation:

-(12x-24)


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
$