1/3x+1/6=7/9x

Solution for 1/3x+1/6=7/9x equation:

1/3x+1/6=7/9x

We move all terms to the left:

1/3x+1/6-(7/9x)=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

1/3x-(+7/9x)+1/6=0

We get rid of parentheses

1/3x-7/9x+1/6=0

We calculate fractions


243x^2/972x^2+324x/972x^2+(-756x)/972x^2=0

We multiply all the terms by the denominator


243x^2+324x+(-756x)=0

We get rid of parentheses

243x^2+324x-756x=0

We add all the numbers together, and all the variables

243x^2-432x=0

a = 243; b = -432; c = 0;
Δ = b2-4ac
Δ = -4322-4·243·0
Δ = 186624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{186624}=432$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-432)-432}{2*243}=\frac{0}{486}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-432)+432}{2*243}=\frac{864}{486}
=1+7/9
$