-5/3v-1/4=5/4v-5

Solution for -5/3v-1/4=5/4v-5 equation:

-5/3v-1/4=5/4v-5

We move all terms to the left:

-5/3v-1/4-(5/4v-5)=0


Domain of the equation: 3v!=0

v!=0/3

v!=0

v∈R



Domain of the equation: 4v-5)!=0

v∈R


We get rid of parentheses

-5/3v-5/4v+5-1/4=0

We calculate fractions


(-320v)/192v^2+(-15v)/192v^2+(-3v)/192v^2+5=0

We multiply all the terms by the denominator


(-320v)+(-15v)+(-3v)+5*192v^2=0

Wy multiply elements

960v^2+(-320v)+(-15v)+(-3v)=0

We get rid of parentheses

960v^2-320v-15v-3v=0

We add all the numbers together, and all the variables

960v^2-338v=0

a = 960; b = -338; c = 0;
Δ = b2-4ac
Δ = -3382-4·960·0
Δ = 114244
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{114244}=338$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-338)-338}{2*960}=\frac{0}{1920}
=0
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-338)+338}{2*960}=\frac{676}{1920}
=169/480
$