x+1/x+6+2/x=2x+1/x+1

Solution for x+1/x+6+2/x=2x+1/x+1 equation:

x+1/x+6+2/x=2x+1/x+1

We move all terms to the left:

x+1/x+6+2/x-(2x+1/x+1)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: x+1)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


x*x-2x*x-1*x+6*x+1+2-1=0

We add all the numbers together, and all the variables

5x+x*x-2x*x+2=0

Wy multiply elements

x^2-2x^2+5x+2=0

We add all the numbers together, and all the variables

-1x^2+5x+2=0

a = -1; b = 5; c = +2;
Δ = b2-4ac
Δ = 52-4·(-1)·2
Δ = 33
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{33}}{2*-1}=\frac{-5-\sqrt{33}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{33}}{2*-1}=\frac{-5+\sqrt{33}}{-2}
$