20/36x=x

Solution for 20/36x=x equation:

20/36x=x

We move all terms to the left:

20/36x-(x)=0


Domain of the equation: 36x!=0

x!=0/36

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+20/36x=0

We multiply all the terms by the denominator


-1x*36x+20=0

Wy multiply elements

-36x^2+20=0

a = -36; b = 0; c = +20;
Δ = b2-4ac
Δ = 02-4·(-36)·20
Δ = 2880
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:

$\sqrt{\Delta}=\sqrt{2880}=\sqrt{576*5}=\sqrt{576}*\sqrt{5}=24\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{5}}{2*-36}=\frac{0-24\sqrt{5}}{-72}
=-\frac{24\sqrt{5}}{-72}
=-\frac{\sqrt{5}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{5}}{2*-36}=\frac{0+24\sqrt{5}}{-72}
=\frac{24\sqrt{5}}{-72}
=\frac{\sqrt{5}}{-3}
$