x-1/x+5+x-1/x-5=2

Solution for x-1/x+5+x-1/x-5=2 equation:

x-1/x+5+x-1/x-5=2

We move all terms to the left:

x-1/x+5+x-1/x-5-(2)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

2x-1/x-1/x-2=0

We multiply all the terms by the denominator


2x*x-2*x-1-1=0

We add all the numbers together, and all the variables

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

Wy multiply elements

2x^2-2x-2=0

a = 2; b = -2; c = -2;
Δ = b2-4ac
Δ = -22-4·2·(-2)
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{5}}{2*2}=\frac{2-2\sqrt{5}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{5}}{2*2}=\frac{2+2\sqrt{5}}{4}
$