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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


9x^2/12x^2+12x/12x^2+(-4x)/12x^2=0

We multiply all the terms by the denominator


9x^2+12x+(-4x)=0

We get rid of parentheses

9x^2+12x-4x=0

We add all the numbers together, and all the variables

9x^2+8x=0

a = 9; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·9·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*9}=\frac{-16}{18}
=-8/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*9}=\frac{0}{18}
=0
$