-9/x=9/3x+9

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

-9/x=9/3x+9

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

-27x^2+(-27x)+(-9x)=0

We get rid of parentheses

-27x^2-27x-9x=0

We add all the numbers together, and all the variables

-27x^2-36x=0

a = -27; b = -36; c = 0;
Δ = b2-4ac
Δ = -362-4·(-27)·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-36}{2*-27}=\frac{0}{-54}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+36}{2*-27}=\frac{72}{-54}
=-1+1/3
$