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

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

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

We move all terms to the left:

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


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

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

We calculate fractions


(-3x)/27x^2+18x/27x^2-5=0

We multiply all the terms by the denominator


(-3x)+18x-5*27x^2=0

We add all the numbers together, and all the variables

18x+(-3x)-5*27x^2=0

Wy multiply elements

-135x^2+18x+(-3x)=0

We get rid of parentheses

-135x^2+18x-3x=0

We add all the numbers together, and all the variables

-135x^2+15x=0

a = -135; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·(-135)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*-135}=\frac{-30}{-270}
=1/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*-135}=\frac{0}{-270}
=0
$