x+3/5x+2=x-4/x

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Solution for x+3/5x+2=x-4/x equation: 



x+3/5x+2=x-4/x

We move all terms to the left:

x+3/5x+2-(x-4/x)=0



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R





Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R



We add all the numbers together, and all the variables

x+3/5x-(+x-4/x)+2=0

We get rid of parentheses

x+3/5x-x+4/x+2=0

We calculate fractions


x-x+3x/5x^2+20x/5x^2+2=0

We add all the numbers together, and all the variables

3x/5x^2+20x/5x^2+2=0

We multiply all the terms by the denominator


3x+20x+2*5x^2=0

We add all the numbers together, and all the variables

23x+2*5x^2=0

Wy multiply elements

10x^2+23x=0

a = 10; b = 23; c = 0;
Δ = b2-4ac
Δ = 232-4·10·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-23}{2*10}=\frac{-46}{20}
=-2+3/10
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+23}{2*10}=\frac{0}{20}
=0
$

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