1/3x-3=1/9x+13

Solution for 1/3x-3=1/9x+13 equation:

1/3x-3=1/9x+13

We move all terms to the left:

1/3x-3-(1/9x+13)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 9x+13)!=0

x∈R


We get rid of parentheses

1/3x-1/9x-13-3=0

We calculate fractions


9x/27x^2+(-3x)/27x^2-13-3=0

We add all the numbers together, and all the variables

9x/27x^2+(-3x)/27x^2-16=0

We multiply all the terms by the denominator


9x+(-3x)-16*27x^2=0

Wy multiply elements

-432x^2+9x+(-3x)=0

We get rid of parentheses

-432x^2+9x-3x=0

We add all the numbers together, and all the variables

-432x^2+6x=0

a = -432; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-432)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-432}=\frac{-12}{-864}
=1/72
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-432}=\frac{0}{-864}
=0
$