-7/4v+16-1=-8/v+4

Solution for -7/4v+16-1=-8/v+4 equation:

-7/4v+16-1=-8/v+4

We move all terms to the left:

-7/4v+16-1-(-8/v+4)=0


Domain of the equation: 4v!=0

v!=0/4

v!=0

v∈R



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

v∈R


We add all the numbers together, and all the variables

-7/4v-(-8/v+4)+15=0

We get rid of parentheses

-7/4v+8/v-4+15=0

We calculate fractions


(-7v)/4v^2+32v/4v^2-4+15=0

We add all the numbers together, and all the variables

(-7v)/4v^2+32v/4v^2+11=0

We multiply all the terms by the denominator


(-7v)+32v+11*4v^2=0

We add all the numbers together, and all the variables

32v+(-7v)+11*4v^2=0

Wy multiply elements

44v^2+32v+(-7v)=0

We get rid of parentheses

44v^2+32v-7v=0

We add all the numbers together, and all the variables

44v^2+25v=0

a = 44; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·44·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*44}=\frac{-50}{88}
=-25/44
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*44}=\frac{0}{88}
=0
$