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

Solution for 4/x-1+1/5x-5=-8 equation:

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

4/x+1/5x+2=0

We calculate fractions


20x/5x^2+x/5x^2+2=0

We multiply all the terms by the denominator


20x+x+2*5x^2=0

We add all the numbers together, and all the variables

21x+2*5x^2=0

Wy multiply elements

10x^2+21x=0

a = 10; b = 21; c = 0;
Δ = b2-4ac
Δ = 212-4·10·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-21}{2*10}=\frac{-42}{20}
=-2+1/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21}{2*10}=\frac{0}{20}
=0
$