(2/3x)-(-5/9x=3)

Solution for (2/3x)-(-5/9x=3) equation:

(2/3x)-(-5/9x=3)

We move all terms to the left:

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


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 9x-3)!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


18x/27x^2+15x/27x^2+3=0

We multiply all the terms by the denominator


18x+15x+3*27x^2=0

We add all the numbers together, and all the variables

33x+3*27x^2=0

Wy multiply elements

81x^2+33x=0

a = 81; b = 33; c = 0;
Δ = b2-4ac
Δ = 332-4·81·0
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-33}{2*81}=\frac{-66}{162}
=-11/27
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+33}{2*81}=\frac{0}{162}
=0
$