1/5v-25+1=-8/v-5

Solution for 1/5v-25+1=-8/v-5 equation:

1/5v-25+1=-8/v-5

We move all terms to the left:

1/5v-25+1-(-8/v-5)=0


Domain of the equation: 5v!=0

v!=0/5

v!=0

v∈R



Domain of the equation: v-5)!=0

v∈R


We add all the numbers together, and all the variables

1/5v-(-8/v-5)-24=0

We get rid of parentheses

1/5v+8/v+5-24=0

We calculate fractions


v/5v^2+40v/5v^2+5-24=0

We add all the numbers together, and all the variables

v/5v^2+40v/5v^2-19=0

We multiply all the terms by the denominator


v+40v-19*5v^2=0

We add all the numbers together, and all the variables

41v-19*5v^2=0

Wy multiply elements

-95v^2+41v=0

a = -95; b = 41; c = 0;
Δ = b2-4ac
Δ = 412-4·(-95)·0
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(41)-41}{2*-95}=\frac{-82}{-190}
=41/95
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+41}{2*-95}=\frac{0}{-190}
=0
$