1/5x-20+1=-8/x-4

Solution for 1/5x-20+1=-8/x-4 equation:

1/5x-20+1=-8/x-4

We move all terms to the left:

1/5x-20+1-(-8/x-4)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: x-4)!=0

x∈R


We add all the numbers together, and all the variables

1/5x-(-8/x-4)-19=0

We get rid of parentheses

1/5x+8/x+4-19=0

We calculate fractions


x/5x^2+40x/5x^2+4-19=0

We add all the numbers together, and all the variables

x/5x^2+40x/5x^2-15=0

We multiply all the terms by the denominator


x+40x-15*5x^2=0

We add all the numbers together, and all the variables

41x-15*5x^2=0

Wy multiply elements

-75x^2+41x=0

a = -75; b = 41; c = 0;
Δ = b2-4ac
Δ = 412-4·(-75)·0
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(41)-41}{2*-75}=\frac{-82}{-150}
=41/75
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+41}{2*-75}=\frac{0}{-150}
=0
$