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2/3x+6=4/2x

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Solution for 2/3x+6=4/2x equation: 



2/3x+6=4/2x

We move all terms to the left:

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

We get rid of parentheses

2/3x-4/2x+6=0

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

36x^2+4x+(-12x)=0

We get rid of parentheses

36x^2+4x-12x=0

We add all the numbers together, and all the variables

36x^2-8x=0

a = 36; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·36·0
Δ = 64
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{64}=8


x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*36}=\frac{0}{72}
=0



x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*36}=\frac{16}{72}
=2/9

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