x+4/x-2*x-6/x+8=1

Solution for x+4/x-2*x-6/x+8=1 equation:

x+4/x-2*x-6/x+8=1

We move all terms to the left:

x+4/x-2*x-6/x+8-(1)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-1x+4/x-6/x+7=0

We multiply all the terms by the denominator


-1x*x+7*x+4-6=0

We add all the numbers together, and all the variables

7x-1x*x-2=0

Wy multiply elements

-1x^2+7x-2=0

a = -1; b = 7; c = -2;
Δ = b2-4ac
Δ = 72-4·(-1)·(-2)
Δ = 41
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{-(7)-\sqrt{41}}{2*-1}=\frac{-7-\sqrt{41}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{41}}{2*-1}=\frac{-7+\sqrt{41}}{-2}
$