5/x+2/3x=1/9

Solution for 5/x+2/3x=1/9 equation:

5/x+2/3x=1/9

We move all terms to the left:

5/x+2/3x-(1/9)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

5/x+2/3x-(+1/9)=0

We get rid of parentheses

5/x+2/3x-1/9=0

We calculate fractions


(-9x^2)/243x^2+1215x/243x^2+162x/243x^2=0

We multiply all the terms by the denominator


(-9x^2)+1215x+162x=0

We add all the numbers together, and all the variables

(-9x^2)+1377x=0

We get rid of parentheses

-9x^2+1377x=0

a = -9; b = 1377; c = 0;
Δ = b2-4ac
Δ = 13772-4·(-9)·0
Δ = 1896129
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1896129}=1377$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1377)-1377}{2*-9}=\frac{-2754}{-18}
=+153
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1377)+1377}{2*-9}=\frac{0}{-18}
=0
$