9/3x+9/x=-9

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

9/3x+9/x=-9

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

9/3x+9/x+9=0

We calculate fractions


9x/3x^2+27x/3x^2+9=0

We multiply all the terms by the denominator


9x+27x+9*3x^2=0

We add all the numbers together, and all the variables

36x+9*3x^2=0

Wy multiply elements

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