4/2x=6/x+2

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Solution for 4/2x=6/x+2 equation:



4/2x=6/x+2
We move all terms to the left:
4/2x-(6/x+2)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: x+2)!=0
x∈R
We get rid of parentheses
4/2x-6/x-2=0
We calculate fractions
4x/2x^2+(-12x)/2x^2-2=0
We multiply all the terms by the denominator
4x+(-12x)-2*2x^2=0
Wy multiply elements
-4x^2+4x+(-12x)=0
We get rid of parentheses
-4x^2+4x-12x=0
We add all the numbers together, and all the variables
-4x^2-8x=0
a = -4; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·(-4)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*-4}=\frac{0}{-8} =0 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*-4}=\frac{16}{-8} =-2 $

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