1/3x+2=-5/9x

Solution for 1/3x+2=-5/9x equation:

1/3x+2=-5/9x

We move all terms to the left:

1/3x+2-(-5/9x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 9x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

1/3x+5/9x+2=0

We calculate fractions


9x/27x^2+15x/27x^2+2=0

We multiply all the terms by the denominator


9x+15x+2*27x^2=0

We add all the numbers together, and all the variables

24x+2*27x^2=0

Wy multiply elements

54x^2+24x=0

a = 54; b = 24; c = 0;
Δ = b2-4ac
Δ = 242-4·54·0
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*54}=\frac{-48}{108}
=-4/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24}{2*54}=\frac{0}{108}
=0
$