2+4/9x=2+x

Solution for 2+4/9x=2+x equation:

2+4/9x=2+x

We move all terms to the left:

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


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


-x*9x-2*9x+2*9x+4=0

Wy multiply elements

-9x^2-18x+18x+4=0

We add all the numbers together, and all the variables

-9x^2+4=0

a = -9; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-9)·4
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{-(0)-12}{2*-9}=\frac{-12}{-18}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12}{2*-9}=\frac{12}{-18}
=-2/3
$