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

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Solution for 2x/x-3+2x-5=0 equation:



2x/x-3+2x-5=0
Domain of the equation: x!=0
x∈R
We add all the numbers together, and all the variables
2x+2x/x-8=0
We multiply all the terms by the denominator
2x*x+2x-8*x=0
We add all the numbers together, and all the variables
-6x+2x*x=0
Wy multiply elements
2x^2-6x=0
a = 2; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·2·0
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{-(-6)-6}{2*2}=\frac{0}{4} =0 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*2}=\frac{12}{4} =3 $

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