2/3x-1=7/9x

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Solution for 2/3x-1=7/9x equation:



2/3x-1=7/9x
We move all terms to the left:
2/3x-1-(7/9x)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 9x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
2/3x-(+7/9x)-1=0
We get rid of parentheses
2/3x-7/9x-1=0
We calculate fractions
18x/27x^2+(-21x)/27x^2-1=0
We multiply all the terms by the denominator
18x+(-21x)-1*27x^2=0
Wy multiply elements
-27x^2+18x+(-21x)=0
We get rid of parentheses
-27x^2+18x-21x=0
We add all the numbers together, and all the variables
-27x^2-3x=0
a = -27; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-27)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-27}=\frac{0}{-54} =0 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-27}=\frac{6}{-54} =-1/9 $

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