(5/x)+(19/5x)-(1/5)=2

Solution for (5/x)+(19/5x)-(1/5)=2 equation:

(5/x)+(19/5x)-(1/5)=2

We move all terms to the left:

(5/x)+(19/5x)-(1/5)-(2)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


determiningTheFunctionDomain
(5/x)+(19/5x)-2-(1/5)=0

We add all the numbers together, and all the variables

(+5/x)+(+19/5x)-2-(+1/5)=0

We get rid of parentheses

5/x+19/5x-2-1/5=0

We calculate fractions


625x/125x^2+19x/125x^2+(-x)/125x^2-2=0

We add all the numbers together, and all the variables

625x/125x^2+19x/125x^2+(-1x)/125x^2-2=0

We multiply all the terms by the denominator


625x+19x+(-1x)-2*125x^2=0

We add all the numbers together, and all the variables

644x+(-1x)-2*125x^2=0

Wy multiply elements

-250x^2+644x+(-1x)=0

We get rid of parentheses

-250x^2+644x-1x=0

We add all the numbers together, and all the variables

-250x^2+643x=0

a = -250; b = 643; c = 0;
Δ = b2-4ac
Δ = 6432-4·(-250)·0
Δ = 413449
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{413449}=643$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(643)-643}{2*-250}=\frac{-1286}{-500}
=2+143/250
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(643)+643}{2*-250}=\frac{0}{-500}
=0
$