5/x+8/5x-1/5=2

Solution for 5/x+8/5x-1/5=2 equation:

5/x+8/5x-1/5=2

We move all terms to the left:

5/x+8/5x-1/5-(2)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


determiningTheFunctionDomain
5/x+8/5x-2-1/5=0

We calculate fractions


625x/125x^2+8x/125x^2+(-x)/125x^2-2=0

We add all the numbers together, and all the variables

625x/125x^2+8x/125x^2+(-1x)/125x^2-2=0

We multiply all the terms by the denominator


625x+8x+(-1x)-2*125x^2=0

We add all the numbers together, and all the variables

633x+(-1x)-2*125x^2=0

Wy multiply elements

-250x^2+633x+(-1x)=0

We get rid of parentheses

-250x^2+633x-1x=0

We add all the numbers together, and all the variables

-250x^2+632x=0

a = -250; b = 632; c = 0;
Δ = b2-4ac
Δ = 6322-4·(-250)·0
Δ = 399424
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{399424}=632$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(632)-632}{2*-250}=\frac{-1264}{-500}
=2+66/125
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(632)+632}{2*-250}=\frac{0}{-500}
=0
$