(2/x)-(3/2x)=1/5

Solution for (2/x)-(3/2x)=1/5 equation:

(2/x)-(3/2x)=1/5

We move all terms to the left:

(2/x)-(3/2x)-(1/5)=0


Domain of the equation: x)!=0

x!=0/1

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

(+2/x)-(+3/2x)-(+1/5)=0

We get rid of parentheses

2/x-3/2x-1/5=0

We calculate fractions


(-4x^2)/50x^2+100x/50x^2+(-75x)/50x^2=0

We multiply all the terms by the denominator


(-4x^2)+100x+(-75x)=0

We get rid of parentheses

-4x^2+100x-75x=0

We add all the numbers together, and all the variables

-4x^2+25x=0

a = -4; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·(-4)·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*-4}=\frac{-50}{-8}
=6+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*-4}=\frac{0}{-8}
=0
$