(1/x)+(1/2x)=4/9

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Solution for (1/x)+(1/2x)=4/9 equation:



(1/x)+(1/2x)=4/9
We move all terms to the left:
(1/x)+(1/2x)-(4/9)=0
Domain of the equation: x)!=0
x!=0/1
x!=0
x∈R
Domain of the equation: 2x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
(+1/x)+(+1/2x)-(+4/9)=0
We get rid of parentheses
1/x+1/2x-4/9=0
We calculate fractions
(-16x^2)/162x^2+162x/162x^2+81x/162x^2=0
We multiply all the terms by the denominator
(-16x^2)+162x+81x=0
We add all the numbers together, and all the variables
(-16x^2)+243x=0
We get rid of parentheses
-16x^2+243x=0
a = -16; b = 243; c = 0;
Δ = b2-4ac
Δ = 2432-4·(-16)·0
Δ = 59049
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{59049}=243$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(243)-243}{2*-16}=\frac{-486}{-32} =15+3/16 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(243)+243}{2*-16}=\frac{0}{-32} =0 $

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