2/3x-5=2/9x+22

Solution for 2/3x-5=2/9x+22 equation:

2/3x-5=2/9x+22

We move all terms to the left:

2/3x-5-(2/9x+22)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 9x+22)!=0

x∈R


We get rid of parentheses

2/3x-2/9x-22-5=0

We calculate fractions


18x/27x^2+(-6x)/27x^2-22-5=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-729x^2+18x+(-6x)=0

We get rid of parentheses

-729x^2+18x-6x=0

We add all the numbers together, and all the variables

-729x^2+12x=0

a = -729; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·(-729)·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*-729}=\frac{-24}{-1458}
=4/243
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*-729}=\frac{0}{-1458}
=0
$