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

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Solution for x+4/x-2*x-6/x+8=0 equation:



x+4/x-2*x-6/x+8=0
Domain of the equation: x!=0
x∈R
We add all the numbers together, and all the variables
-1x+4/x-6/x+8=0
We multiply all the terms by the denominator
-1x*x+8*x+4-6=0
We add all the numbers together, and all the variables
8x-1x*x-2=0
Wy multiply elements
-1x^2+8x-2=0
a = -1; b = 8; c = -2;
Δ = b2-4ac
Δ = 82-4·(-1)·(-2)
Δ = 56
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:
$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{14}}{2*-1}=\frac{-8-2\sqrt{14}}{-2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{14}}{2*-1}=\frac{-8+2\sqrt{14}}{-2} $

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