x-3/x=2/x+4

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



x-3/x=2/x+4
We move all terms to the left:
x-3/x-(2/x+4)=0
Domain of the equation: x!=0
x∈R
Domain of the equation: x+4)!=0
x∈R
We get rid of parentheses
x-3/x-2/x-4=0
We multiply all the terms by the denominator
x*x-4*x-3-2=0
We add all the numbers together, and all the variables
-4x+x*x-5=0
Wy multiply elements
x^2-4x-5=0
a = 1; b = -4; c = -5;
Δ = b2-4ac
Δ = -42-4·1·(-5)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-6}{2*1}=\frac{-2}{2} =-1 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+6}{2*1}=\frac{10}{2} =5 $

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