1/5x-5/x=5

Solution for 1/5x-5/x=5 equation:

1/5x-5/x=5

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: x!=0

x∈R


We calculate fractions


x/5x^2+(-25x)/5x^2-5=0

We multiply all the terms by the denominator


x+(-25x)-5*5x^2=0

Wy multiply elements

-25x^2+x+(-25x)=0

We get rid of parentheses

-25x^2+x-25x=0

We add all the numbers together, and all the variables

-25x^2-24x=0

a = -25; b = -24; c = 0;
Δ = b2-4ac
Δ = -242-4·(-25)·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-24}{2*-25}=\frac{0}{-50}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+24}{2*-25}=\frac{48}{-50}
=-24/25
$