2x-8/x=x+8/x+5

Solution for 2x-8/x=x+8/x+5 equation:

2x-8/x=x+8/x+5

We move all terms to the left:

2x-8/x-(x+8/x+5)=0


Domain of the equation: x!=0

x∈R



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

x∈R


We get rid of parentheses

2x-8/x-x-8/x-5=0

We multiply all the terms by the denominator


2x*x-x*x-5*x-8-8=0

We add all the numbers together, and all the variables

-5x+2x*x-x*x-16=0

Wy multiply elements

2x^2-1x^2-5x-16=0

We add all the numbers together, and all the variables

x^2-5x-16=0

a = 1; b = -5; c = -16;
Δ = b2-4ac
Δ = -52-4·1·(-16)
Δ = 89
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{89}}{2*1}=\frac{5-\sqrt{89}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{89}}{2*1}=\frac{5+\sqrt{89}}{2}
$