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

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

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

We move all terms to the left:

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


Domain of the equation: 6x+1)!=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

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

We get rid of parentheses

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

We calculate fractions


6x/6x^2+6x/6x^2+1-9=0

We add all the numbers together, and all the variables

6x/6x^2+6x/6x^2-8=0

We multiply all the terms by the denominator


6x+6x-8*6x^2=0

We add all the numbers together, and all the variables

12x-8*6x^2=0

Wy multiply elements

-48x^2+12x=0

a = -48; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·(-48)·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*-48}=\frac{-24}{-96}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*-48}=\frac{0}{-96}
=0
$