x+1/x=-5

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

x+1/x=-5

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+1/x+5=0

We multiply all the terms by the denominator


x*x+5*x+1=0

We add all the numbers together, and all the variables

5x+x*x+1=0

Wy multiply elements

x^2+5x+1=0

a = 1; b = 5; c = +1;
Δ = b2-4ac
Δ = 52-4·1·1
Δ = 21
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{21}}{2*1}=\frac{-5-\sqrt{21}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{21}}{2*1}=\frac{-5+\sqrt{21}}{2}
$