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

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
$