x+9/6x+1=x+6/x

Solution for x+9/6x+1=x+6/x equation:

x+9/6x+1=x+6/x

We move all terms to the left:

x+9/6x+1-(x+6/x)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x+9/6x-(+x+6/x)+1=0

We get rid of parentheses

x+9/6x-x-6/x+1=0

We calculate fractions


x-x+9x/6x^2+(-36x)/6x^2+1=0

We add all the numbers together, and all the variables

9x/6x^2+(-36x)/6x^2+1=0

We multiply all the terms by the denominator


9x+(-36x)+1*6x^2=0

Wy multiply elements

6x^2+9x+(-36x)=0

We get rid of parentheses

6x^2+9x-36x=0

We add all the numbers together, and all the variables

6x^2-27x=0

a = 6; b = -27; c = 0;
Δ = b2-4ac
Δ = -272-4·6·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-27}{2*6}=\frac{0}{12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+27}{2*6}=\frac{54}{12}
=4+1/2
$