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

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

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

We move all terms to the left:

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


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

2/9x-2/3x-4=0

We calculate fractions


6x/27x^2+(-18x)/27x^2-4=0

We multiply all the terms by the denominator


6x+(-18x)-4*27x^2=0

Wy multiply elements

-108x^2+6x+(-18x)=0

We get rid of parentheses

-108x^2+6x-18x=0

We add all the numbers together, and all the variables

-108x^2-12x=0

a = -108; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·(-108)·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*-108}=\frac{0}{-216}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*-108}=\frac{24}{-216}
=-1/9
$