x=9+1+1/9x

Solution for x=9+1+1/9x equation:

x=9+1+1/9x

We move all terms to the left:

x-(9+1+1/9x)=0


Domain of the equation: 9x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(1/9x+10)=0

We get rid of parentheses

x-1/9x-10=0

We multiply all the terms by the denominator


x*9x-10*9x-1=0

Wy multiply elements

9x^2-90x-1=0

a = 9; b = -90; c = -1;
Δ = b2-4ac
Δ = -902-4·9·(-1)
Δ = 8136
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:

$\sqrt{\Delta}=\sqrt{8136}=\sqrt{36*226}=\sqrt{36}*\sqrt{226}=6\sqrt{226}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-6\sqrt{226}}{2*9}=\frac{90-6\sqrt{226}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+6\sqrt{226}}{2*9}=\frac{90+6\sqrt{226}}{18}
$