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

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

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

We move all terms to the left:

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


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

x∈R


We multiply parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-6x*3x+12*3x-3))-(4(-1))=0

We add all the numbers together, and all the variables

-6x*3x+12*3x=0

Wy multiply elements

-18x^2+36x=0

a = -18; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·(-18)·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-36}{2*-18}=\frac{-72}{-36}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*-18}=\frac{0}{-36}
=0
$