-8/v-5=-5/2v-10+4

Solution for -8/v-5=-5/2v-10+4 equation:

-8/v-5=-5/2v-10+4

We move all terms to the left:

-8/v-5-(-5/2v-10+4)=0


Domain of the equation: v!=0

v∈R



Domain of the equation: 2v-10+4)!=0

We move all terms containing v to the left, all other terms to the right

2v+4)!=10

v∈R


We add all the numbers together, and all the variables

-8/v-(-5/2v-6)-5=0

We get rid of parentheses

-8/v+5/2v+6-5=0

We calculate fractions


(-16v)/2v^2+5v/2v^2+6-5=0

We add all the numbers together, and all the variables

(-16v)/2v^2+5v/2v^2+1=0

We multiply all the terms by the denominator


(-16v)+5v+1*2v^2=0

We add all the numbers together, and all the variables

5v+(-16v)+1*2v^2=0

Wy multiply elements

2v^2+5v+(-16v)=0

We get rid of parentheses

2v^2+5v-16v=0

We add all the numbers together, and all the variables

2v^2-11v=0

a = 2; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·2·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-11}{2*2}=\frac{0}{4}
=0
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*2}=\frac{22}{4}
=5+1/2
$