5x-8/x+2=5-6/x-2

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Solution for 5x-8/x+2=5-6/x-2 equation: 



5x-8/x+2=5-6/x-2

We move all terms to the left:

5x-8/x+2-(5-6/x-2)=0



Domain of the equation: x!=0

x∈R





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

x∈R



We add all the numbers together, and all the variables

5x-8/x-(-6/x+3)+2=0

We get rid of parentheses

5x-8/x+6/x-3+2=0

We multiply all the terms by the denominator


5x*x-3*x+2*x-8+6=0

We add all the numbers together, and all the variables

-1x+5x*x-2=0

Wy multiply elements

5x^2-1x-2=0

a = 5; b = -1; c = -2;
Δ = b2-4ac
Δ = -12-4·5·(-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{-(-1)-\sqrt{41}}{2*5}=\frac{1-\sqrt{41}}{10}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{41}}{2*5}=\frac{1+\sqrt{41}}{10}
$

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