-5/4v-16=7/v-4

Solution for -5/4v-16=7/v-4 equation:

-5/4v-16=7/v-4

We move all terms to the left:

-5/4v-16-(7/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 get rid of parentheses

-5/4v-7/v+4-16=0

We calculate fractions


(-5v)/4v^2+(-28v)/4v^2+4-16=0

We add all the numbers together, and all the variables

(-5v)/4v^2+(-28v)/4v^2-12=0

We multiply all the terms by the denominator


(-5v)+(-28v)-12*4v^2=0

Wy multiply elements

-48v^2+(-5v)+(-28v)=0

We get rid of parentheses

-48v^2-5v-28v=0

We add all the numbers together, and all the variables

-48v^2-33v=0

a = -48; b = -33; c = 0;
Δ = b2-4ac
Δ = -332-4·(-48)·0
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-33}{2*-48}=\frac{0}{-96}
=0
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+33}{2*-48}=\frac{66}{-96}
=-11/16
$