2x+(1/x)=-5

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

2x+(1/x)=-5

We move all terms to the left:

2x+(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

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

2x+1/x+5=0

We multiply all the terms by the denominator


2x*x+5*x+1=0

We add all the numbers together, and all the variables

5x+2x*x+1=0

Wy multiply elements

2x^2+5x+1=0

a = 2; b = 5; c = +1;
Δ = b2-4ac
Δ = 52-4·2·1
Δ = 17
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{17}}{2*2}=\frac{-5-\sqrt{17}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{17}}{2*2}=\frac{-5+\sqrt{17}}{4}
$