2+4/9x=4+x

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

2+4/9x=4+x

We move all terms to the left:

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-9x^2-36x+18x+4=0

We add all the numbers together, and all the variables

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

a = -9; b = -18; c = +4;
Δ = b2-4ac
Δ = -182-4·(-9)·4
Δ = 468
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{468}=\sqrt{36*13}=\sqrt{36}*\sqrt{13}=6\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{13}}{2*-9}=\frac{18-6\sqrt{13}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{13}}{2*-9}=\frac{18+6\sqrt{13}}{-18}
$