2-4/9x=x

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

2-4/9x=x

We move all terms to the left:

2-4/9x-(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

-1x-4/9x+2=0

We multiply all the terms by the denominator


-1x*9x+2*9x-4=0

Wy multiply elements

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

a = -9; b = 18; c = -4;
Δ = b2-4ac
Δ = 182-4·(-9)·(-4)
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6\sqrt{5}}{2*-9}=\frac{-18-6\sqrt{5}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6\sqrt{5}}{2*-9}=\frac{-18+6\sqrt{5}}{-18}
$