1/x-5+3=x+1/x-5

Solution for 1/x-5+3=x+1/x-5 equation:

1/x-5+3=x+1/x-5

We move all terms to the left:

1/x-5+3-(x+1/x-5)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: x-5)!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

3x-x*x=0

Wy multiply elements

-1x^2+3x=0

a = -1; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-1)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-1}=\frac{-6}{-2}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-1}=\frac{0}{-2}
=0
$