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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


27x/54x^2+(-4x)/54x^2+8x/54x^2+2=0

We multiply all the terms by the denominator


27x+(-4x)+8x+2*54x^2=0

We add all the numbers together, and all the variables

35x+(-4x)+2*54x^2=0

Wy multiply elements

108x^2+35x+(-4x)=0

We get rid of parentheses

108x^2+35x-4x=0

We add all the numbers together, and all the variables

108x^2+31x=0

a = 108; b = 31; c = 0;
Δ = b2-4ac
Δ = 312-4·108·0
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-31}{2*108}=\frac{-62}{216}
=-31/108
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+31}{2*108}=\frac{0}{216}
=0
$