x=2/x-2=4/8

Solution for x=2/x-2=4/8 equation:

x=2/x-2=4/8

We move all terms to the left:

x-(2/x-2)=0


Domain of the equation: x-2)!=0

x∈R


We get rid of parentheses

x-2/x+2=0

We multiply all the terms by the denominator


x*x+2*x-2=0

We add all the numbers together, and all the variables

2x+x*x-2=0

Wy multiply elements

x^2+2x-2=0

a = 1; b = 2; c = -2;
Δ = b2-4ac
Δ = 22-4·1·(-2)
Δ = 12
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:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{3}}{2*1}=\frac{-2-2\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{3}}{2*1}=\frac{-2+2\sqrt{3}}{2}
$