2/3x+40=-2/9x

Solution for 2/3x+40=-2/9x equation:

2/3x+40=-2/9x

We move all terms to the left:

2/3x+40-(-2/9x)=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

2/3x+2/9x+40=0

We calculate fractions


18x/27x^2+6x/27x^2+40=0

We multiply all the terms by the denominator


18x+6x+40*27x^2=0

We add all the numbers together, and all the variables

24x+40*27x^2=0

Wy multiply elements

1080x^2+24x=0

a = 1080; b = 24; c = 0;
Δ = b2-4ac
Δ = 242-4·1080·0
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*1080}=\frac{-48}{2160}
=-1/45
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24}{2*1080}=\frac{0}{2160}
=0
$