27/3x-3=27/9x+3

Solution for 27/3x-3=27/9x+3 equation:

27/3x-3=27/9x+3

We move all terms to the left:

27/3x-3-(27/9x+3)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 9x+3)!=0

x∈R


We get rid of parentheses

27/3x-27/9x-3-3=0

We calculate fractions


243x/27x^2+(-81x)/27x^2-3-3=0

We add all the numbers together, and all the variables

243x/27x^2+(-81x)/27x^2-6=0

We multiply all the terms by the denominator


243x+(-81x)-6*27x^2=0

Wy multiply elements

-162x^2+243x+(-81x)=0

We get rid of parentheses

-162x^2+243x-81x=0

We add all the numbers together, and all the variables

-162x^2+162x=0

a = -162; b = 162; c = 0;
Δ = b2-4ac
Δ = 1622-4·(-162)·0
Δ = 26244
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{26244}=162$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(162)-162}{2*-162}=\frac{-324}{-324}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(162)+162}{2*-162}=\frac{0}{-324}
=0
$