5/9x=x

Solution for 5/9x=x equation:

5/9x=x

We move all terms to the left:

5/9x-(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+5/9x=0

We multiply all the terms by the denominator


-1x*9x+5=0

Wy multiply elements

-9x^2+5=0

a = -9; b = 0; c = +5;
Δ = b2-4ac
Δ = 02-4·(-9)·5
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{-(0)-6\sqrt{5}}{2*-9}=\frac{0-6\sqrt{5}}{-18}
=-\frac{6\sqrt{5}}{-18}
=-\frac{\sqrt{5}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{5}}{2*-9}=\frac{0+6\sqrt{5}}{-18}
=\frac{6\sqrt{5}}{-18}
=\frac{\sqrt{5}}{-3}
$