1/x+2/9x=-3

Solution for 1/x+2/9x=-3 equation:

1/x+2/9x=-3

We move all terms to the left:

1/x+2/9x-(-3)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We add all the numbers together, and all the variables

1/x+2/9x+3=0

We calculate fractions


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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

11x+3*9x^2=0

Wy multiply elements

27x^2+11x=0

a = 27; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·27·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*27}=\frac{-22}{54}
=-11/27
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*27}=\frac{0}{54}
=0
$