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!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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}
$