1/x-(1/3x)=1/9

Solution for 1/x-(1/3x)=1/9 equation:

1/x-(1/3x)=1/9

We move all terms to the left:

1/x-(1/3x)-(1/9)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

1/x-1/3x-1/9=0

We calculate fractions


(-9x^2)/243x^2+243x/243x^2+(-81x)/243x^2=0

We multiply all the terms by the denominator


(-9x^2)+243x+(-81x)=0

We get rid of parentheses

-9x^2+243x-81x=0

We add all the numbers together, and all the variables

-9x^2+162x=0

a = -9; b = 162; c = 0;
Δ = b2-4ac
Δ = 1622-4·(-9)·0
Δ = 26244
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{26244}=162$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(162)-162}{2*-9}=\frac{-324}{-18}
=+18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(162)+162}{2*-9}=\frac{0}{-18}
=0
$