x-5/x+5/5=-2/x

Solution for x-5/x+5/5=-2/x equation:

x-5/x+5/5=-2/x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

x+x*x-3=0

Wy multiply elements

x^2+x-3=0

a = 1; b = 1; c = -3;
Δ = b2-4ac
Δ = 12-4·1·(-3)
Δ = 13
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{-(1)-\sqrt{13}}{2*1}=\frac{-1-\sqrt{13}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{13}}{2*1}=\frac{-1+\sqrt{13}}{2}
$