3(3/4x-4)=2(1/3x-6)

Solution for 3(3/4x-4)=2(1/3x-6) equation:

3(3/4x-4)=2(1/3x-6)

We move all terms to the left:

3(3/4x-4)-(2(1/3x-6))=0


Domain of the equation: 4x-4)!=0

x∈R



Domain of the equation: 3x-6))!=0

x∈R


We multiply parentheses

9x-(2(1/3x-6))-12=0

We multiply all the terms by the denominator


9x*3x-12*3x-6))-(2(1-6))=0

We add all the numbers together, and all the variables

9x*3x-12*3x-6))-(2(-5))=0

We add all the numbers together, and all the variables

9x*3x-12*3x=0

Wy multiply elements

27x^2-36x=0

a = 27; b = -36; c = 0;
Δ = b2-4ac
Δ = -362-4·27·0
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*27}=\frac{0}{54}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+36}{2*27}=\frac{72}{54}
=1+1/3
$