(6/x)+x=-5

Solution for (6/x)+x=-5 equation:

(6/x)+x=-5

We move all terms to the left:

(6/x)+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

(+6/x)+x-(-5)=0

We add all the numbers together, and all the variables

x+(+6/x)+5=0

We get rid of parentheses

x+6/x+5=0

We multiply all the terms by the denominator


x*x+5*x+6=0

We add all the numbers together, and all the variables

5x+x*x+6=0

Wy multiply elements

x^2+5x+6=0

a = 1; b = 5; c = +6;
Δ = b2-4ac
Δ = 52-4·1·6
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-1}{2*1}=\frac{-6}{2}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+1}{2*1}=\frac{-4}{2}
=-2
$