x=18-1/36x

Solution for x=18-1/36x equation:

x=18-1/36x

We move all terms to the left:

x-(18-1/36x)=0


Domain of the equation: 36x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(-1/36x+18)=0

We get rid of parentheses

x+1/36x-18=0

We multiply all the terms by the denominator


x*36x-18*36x+1=0

Wy multiply elements

36x^2-648x+1=0

a = 36; b = -648; c = +1;
Δ = b2-4ac
Δ = -6482-4·36·1
Δ = 419760
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:

$\sqrt{\Delta}=\sqrt{419760}=\sqrt{144*2915}=\sqrt{144}*\sqrt{2915}=12\sqrt{2915}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-648)-12\sqrt{2915}}{2*36}=\frac{648-12\sqrt{2915}}{72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-648)+12\sqrt{2915}}{2*36}=\frac{648+12\sqrt{2915}}{72}
$