1/3x+7=2/9x-6

Solution for 1/3x+7=2/9x-6 equation:

1/3x+7=2/9x-6

We move all terms to the left:

1/3x+7-(2/9x-6)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 9x-6)!=0

x∈R


We get rid of parentheses

1/3x-2/9x+6+7=0

We calculate fractions


9x/27x^2+(-6x)/27x^2+6+7=0

We add all the numbers together, and all the variables

9x/27x^2+(-6x)/27x^2+13=0

We multiply all the terms by the denominator


9x+(-6x)+13*27x^2=0

Wy multiply elements

351x^2+9x+(-6x)=0

We get rid of parentheses

351x^2+9x-6x=0

We add all the numbers together, and all the variables

351x^2+3x=0

a = 351; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·351·0
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*351}=\frac{-6}{702}
=-1/117
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*351}=\frac{0}{702}
=0
$