3x(-4x+8)=3(2x-4)

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

3x(-4x+8)=3(2x-4)

We move all terms to the left:

3x(-4x+8)-(3(2x-4))=0

We multiply parentheses

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


We calculate terms in parentheses: -(3(2x-4)), so:

3(2x-4)

We multiply parentheses

6x-12

Back to the equation:

-(6x-12)


We get rid of parentheses

-12x^2+24x-6x+12=0

We add all the numbers together, and all the variables

-12x^2+18x+12=0

a = -12; b = 18; c = +12;
Δ = b2-4ac
Δ = 182-4·(-12)·12
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-30}{2*-12}=\frac{-48}{-24}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+30}{2*-12}=\frac{12}{-24}
=-1/2
$