8/x+2=x+4/x-6

Solution for 8/x+2=x+4/x-6 equation:

8/x+2=x+4/x-6

We move all terms to the left:

8/x+2-(x+4/x-6)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: x-6)!=0

x∈R


We get rid of parentheses

8/x-x-4/x+6+2=0

We multiply all the terms by the denominator


-x*x+6*x+2*x+8-4=0

We add all the numbers together, and all the variables

8x-x*x+4=0

Wy multiply elements

-1x^2+8x+4=0

a = -1; b = 8; c = +4;
Δ = b2-4ac
Δ = 82-4·(-1)·4
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{5}}{2*-1}=\frac{-8-4\sqrt{5}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{5}}{2*-1}=\frac{-8+4\sqrt{5}}{-2}
$