x+2/x-2=8

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

x+2/x-2=8

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+2/x-10=0

We multiply all the terms by the denominator


x*x-10*x+2=0

We add all the numbers together, and all the variables

-10x+x*x+2=0

Wy multiply elements

x^2-10x+2=0

a = 1; b = -10; c = +2;
Δ = b2-4ac
Δ = -102-4·1·2
Δ = 92
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{92}=\sqrt{4*23}=\sqrt{4}*\sqrt{23}=2\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{23}}{2*1}=\frac{10-2\sqrt{23}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{23}}{2*1}=\frac{10+2\sqrt{23}}{2}
$