1/x-2/3=3/2x

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

1/x-2/3=3/2x

We move all terms to the left:

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


Domain of the equation: 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-(+3/2x)-2/3=0

We get rid of parentheses

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

We calculate fractions


(-8x^2)/18x^2+18x/18x^2+(-27x)/18x^2=0

We multiply all the terms by the denominator


(-8x^2)+18x+(-27x)=0

We get rid of parentheses

-8x^2+18x-27x=0

We add all the numbers together, and all the variables

-8x^2-9x=0

a = -8; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·(-8)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*-8}=\frac{0}{-16}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*-8}=\frac{18}{-16}
=-1+1/8
$