(3/2x)-(5/x)=65

Solution for (3/2x)-(5/x)=65 equation:

(3/2x)-(5/x)=65

We move all terms to the left:

(3/2x)-(5/x)-(65)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+3/2x)-(+5/x)-65=0

We get rid of parentheses

3/2x-5/x-65=0

We calculate fractions


3x/2x^2+(-10x)/2x^2-65=0

We multiply all the terms by the denominator


3x+(-10x)-65*2x^2=0

Wy multiply elements

-130x^2+3x+(-10x)=0

We get rid of parentheses

-130x^2+3x-10x=0

We add all the numbers together, and all the variables

-130x^2-7x=0

a = -130; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·(-130)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*-130}=\frac{0}{-260}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*-130}=\frac{14}{-260}
=-7/130
$