2/3x-4/3=1-3/2x

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

2/3x-4/3=1-3/2x

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

2/3x+3/2x-1-4/3=0

We calculate fractions


4x/54x^2+81x/54x^2+(-8x)/54x^2-1=0

We multiply all the terms by the denominator


4x+81x+(-8x)-1*54x^2=0

We add all the numbers together, and all the variables

85x+(-8x)-1*54x^2=0

Wy multiply elements

-54x^2+85x+(-8x)=0

We get rid of parentheses

-54x^2+85x-8x=0

We add all the numbers together, and all the variables

-54x^2+77x=0

a = -54; b = 77; c = 0;
Δ = b2-4ac
Δ = 772-4·(-54)·0
Δ = 5929
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5929}=77$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(77)-77}{2*-54}=\frac{-154}{-108}
=1+23/54
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(77)+77}{2*-54}=\frac{0}{-108}
=0
$