1/x+1/2x=2/3

Solution for 1/x+1/2x=2/3 equation:

1/x+1/2x=2/3

We move all terms to the left:

1/x+1/2x-(2/3)=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

1/x+1/2x-(+2/3)=0

We get rid of parentheses

1/x+1/2x-2/3=0

We calculate fractions


(-8x^2)/18x^2+18x/18x^2+9x/18x^2=0

We multiply all the terms by the denominator


(-8x^2)+18x+9x=0

We add all the numbers together, and all the variables

(-8x^2)+27x=0

We get rid of parentheses

-8x^2+27x=0

a = -8; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·(-8)·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-27}{2*-8}=\frac{-54}{-16}
=3+3/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*-8}=\frac{0}{-16}
=0
$