-5/2v+12+1=-8/v+6

Solution for -5/2v+12+1=-8/v+6 equation:

-5/2v+12+1=-8/v+6

We move all terms to the left:

-5/2v+12+1-(-8/v+6)=0


Domain of the equation: 2v!=0

v!=0/2

v!=0

v∈R



Domain of the equation: v+6)!=0

v∈R


We add all the numbers together, and all the variables

-5/2v-(-8/v+6)+13=0

We get rid of parentheses

-5/2v+8/v-6+13=0

We calculate fractions


(-5v)/2v^2+16v/2v^2-6+13=0

We add all the numbers together, and all the variables

(-5v)/2v^2+16v/2v^2+7=0

We multiply all the terms by the denominator


(-5v)+16v+7*2v^2=0

We add all the numbers together, and all the variables

16v+(-5v)+7*2v^2=0

Wy multiply elements

14v^2+16v+(-5v)=0

We get rid of parentheses

14v^2+16v-5v=0

We add all the numbers together, and all the variables

14v^2+11v=0

a = 14; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·14·0
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*14}=\frac{-22}{28}
=-11/14
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*14}=\frac{0}{28}
=0
$