4/3x+3=-5/9x-2

Solution for 4/3x+3=-5/9x-2 equation:

4/3x+3=-5/9x-2

We move all terms to the left:

4/3x+3-(-5/9x-2)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 9x-2)!=0

x∈R


We get rid of parentheses

4/3x+5/9x+2+3=0

We calculate fractions


36x/27x^2+15x/27x^2+2+3=0

We add all the numbers together, and all the variables

36x/27x^2+15x/27x^2+5=0

We multiply all the terms by the denominator


36x+15x+5*27x^2=0

We add all the numbers together, and all the variables

51x+5*27x^2=0

Wy multiply elements

135x^2+51x=0

a = 135; b = 51; c = 0;
Δ = b2-4ac
Δ = 512-4·135·0
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-51}{2*135}=\frac{-102}{270}
=-17/45
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+51}{2*135}=\frac{0}{270}
=0
$