3/9x-8=3/x+5

Solution for 3/9x-8=3/x+5 equation:

3/9x-8=3/x+5

We move all terms to the left:

3/9x-8-(3/x+5)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: x+5)!=0

x∈R


We get rid of parentheses

3/9x-3/x-5-8=0

We calculate fractions


3x/9x^2+(-27x)/9x^2-5-8=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-117x^2+3x+(-27x)=0

We get rid of parentheses

-117x^2+3x-27x=0

We add all the numbers together, and all the variables

-117x^2-24x=0

a = -117; b = -24; c = 0;
Δ = b2-4ac
Δ = -242-4·(-117)·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-24}{2*-117}=\frac{0}{-234}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+24}{2*-117}=\frac{48}{-234}
=-8/39
$