1/3x-5/9x=5

Solution for 1/3x-5/9x=5 equation:

1/3x-5/9x=5

We move all terms to the left:

1/3x-5/9x-(5)=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 calculate fractions


9x/27x^2+(-15x)/27x^2-5=0

We multiply all the terms by the denominator


9x+(-15x)-5*27x^2=0

Wy multiply elements

-135x^2+9x+(-15x)=0

We get rid of parentheses

-135x^2+9x-15x=0

We add all the numbers together, and all the variables

-135x^2-6x=0

a = -135; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·(-135)·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*-135}=\frac{0}{-270}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*-135}=\frac{12}{-270}
=-2/45
$