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

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

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

We move all terms to the left:

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

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

We get rid of parentheses

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

We calculate fractions


(-16x^2)/24x^2+48x/24x^2+27x/24x^2+(-9x)/24x^2=0

We multiply all the terms by the denominator


(-16x^2)+48x+27x+(-9x)=0

We add all the numbers together, and all the variables

(-16x^2)+75x+(-9x)=0

We get rid of parentheses

-16x^2+75x-9x=0

We add all the numbers together, and all the variables

-16x^2+66x=0

a = -16; b = 66; c = 0;
Δ = b2-4ac
Δ = 662-4·(-16)·0
Δ = 4356
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4356}=66$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(66)-66}{2*-16}=\frac{-132}{-32}
=4+1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(66)+66}{2*-16}=\frac{0}{-32}
=0
$