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

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Solution for 4/x-4-2/2x-5=0 equation:



4/x-4-2/2x-5=0
Domain of the equation: x!=0
x∈R
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
We add all the numbers together, and all the variables
4/x-2/2x-9=0
We calculate fractions
8x/2x^2+(-2x)/2x^2-9=0
We multiply all the terms by the denominator
8x+(-2x)-9*2x^2=0
Wy multiply elements
-18x^2+8x+(-2x)=0
We get rid of parentheses
-18x^2+8x-2x=0
We add all the numbers together, and all the variables
-18x^2+6x=0
a = -18; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-18)·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*-18}=\frac{-12}{-36} =1/3 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-18}=\frac{0}{-36} =0 $

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