(x+1/x+5)=1

Solution for (x+1/x+5)=1 equation:

(x+1/x+5)=1

We move all terms to the left:

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


Domain of the equation: x+5)!=0

x∈R


We get rid of parentheses

x+1/x+5-1=0

We multiply all the terms by the denominator


x*x+5*x-1*x+1=0

We add all the numbers together, and all the variables

4x+x*x+1=0

Wy multiply elements

x^2+4x+1=0

a = 1; b = 4; c = +1;
Δ = b2-4ac
Δ = 42-4·1·1
Δ = 12
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:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{3}}{2*1}=\frac{-4-2\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{3}}{2*1}=\frac{-4+2\sqrt{3}}{2}
$