-3(2x-4)=4(-3/2x-3)

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

-3(2x-4)=4(-3/2x-3)

We move all terms to the left:

-3(2x-4)-(4(-3/2x-3))=0


Domain of the equation: 2x-3))!=0

x∈R


We multiply parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-6x*2x+12*2x=0

Wy multiply elements

-12x^2+24x=0

a = -12; b = 24; c = 0;
Δ = b2-4ac
Δ = 242-4·(-12)·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24}{2*-12}=\frac{-48}{-24}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24}{2*-12}=\frac{0}{-24}
=0
$