(2/3x)-(5/9x)=5

Solution for (2/3x)-(5/9x)=5 equation:

(2/3x)-(5/9x)=5

We move all terms to the left:

(2/3x)-(5/9x)-(5)=0


Domain of the equation: 3x)!=0

x!=0/1

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)-5=0

We get rid of parentheses

2/3x-5/9x-5=0

We calculate fractions


18x/27x^2+(-15x)/27x^2-5=0

We multiply all the terms by the denominator


18x+(-15x)-5*27x^2=0

Wy multiply elements

-135x^2+18x+(-15x)=0

We get rid of parentheses

-135x^2+18x-15x=0

We add all the numbers together, and all the variables

-135x^2+3x=0

a = -135; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-135)·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*-135}=\frac{-6}{-270}
=1/45
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-135}=\frac{0}{-270}
=0
$