1/3x-1/9x=1/18

Solution for 1/3x-1/9x=1/18 equation:

1/3x-1/9x=1/18

We move all terms to the left:

1/3x-1/9x-(1/18)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We add all the numbers together, and all the variables

1/3x-1/9x-(+1/18)=0

We get rid of parentheses

1/3x-1/9x-1/18=0

We calculate fractions


(-243x^2)/486x^2+162x/486x^2+(-54x)/486x^2=0

We multiply all the terms by the denominator


(-243x^2)+162x+(-54x)=0

We get rid of parentheses

-243x^2+162x-54x=0

We add all the numbers together, and all the variables

-243x^2+108x=0

a = -243; b = 108; c = 0;
Δ = b2-4ac
Δ = 1082-4·(-243)·0
Δ = 11664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11664}=108$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(108)-108}{2*-243}=\frac{-216}{-486}
=4/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(108)+108}{2*-243}=\frac{0}{-486}
=0
$