2/3x-5=4+5/9x

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Solution for 2/3x-5=4+5/9x equation:



2/3x-5=4+5/9x
We move all terms to the left:
2/3x-5-(4+5/9x)=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-(5/9x+4)-5=0
We get rid of parentheses
2/3x-5/9x-4-5=0
We calculate fractions
18x/27x^2+(-15x)/27x^2-4-5=0
We add all the numbers together, and all the variables
18x/27x^2+(-15x)/27x^2-9=0
We multiply all the terms by the denominator
18x+(-15x)-9*27x^2=0
Wy multiply elements
-243x^2+18x+(-15x)=0
We get rid of parentheses
-243x^2+18x-15x=0
We add all the numbers together, and all the variables
-243x^2+3x=0
a = -243; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-243)·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*-243}=\frac{-6}{-486} =1/81 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-243}=\frac{0}{-486} =0 $

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