2/3x-4+9=4/9x-6

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Solution for 2/3x-4+9=4/9x-6 equation:



2/3x-4+9=4/9x-6
We move all terms to the left:
2/3x-4+9-(4/9x-6)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 9x-6)!=0
x∈R
We add all the numbers together, and all the variables
2/3x-(4/9x-6)+5=0
We get rid of parentheses
2/3x-4/9x+6+5=0
We calculate fractions
18x/27x^2+(-12x)/27x^2+6+5=0
We add all the numbers together, and all the variables
18x/27x^2+(-12x)/27x^2+11=0
We multiply all the terms by the denominator
18x+(-12x)+11*27x^2=0
Wy multiply elements
297x^2+18x+(-12x)=0
We get rid of parentheses
297x^2+18x-12x=0
We add all the numbers together, and all the variables
297x^2+6x=0
a = 297; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·297·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*297}=\frac{-12}{594} =-2/99 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*297}=\frac{0}{594} =0 $

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