5/4v+4+1/3v=8

Solution for 5/4v+4+1/3v=8 equation:

5/4v+4+1/3v=8

We move all terms to the left:

5/4v+4+1/3v-(8)=0


Domain of the equation: 4v!=0

v!=0/4

v!=0

v∈R



Domain of the equation: 3v!=0

v!=0/3

v!=0

v∈R


We add all the numbers together, and all the variables

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

We calculate fractions


15v/12v^2+4v/12v^2-4=0

We multiply all the terms by the denominator


15v+4v-4*12v^2=0

We add all the numbers together, and all the variables

19v-4*12v^2=0

Wy multiply elements

-48v^2+19v=0

a = -48; b = 19; c = 0;
Δ = b2-4ac
Δ = 192-4·(-48)·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-19}{2*-48}=\frac{-38}{-96}
=19/48
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+19}{2*-48}=\frac{0}{-96}
=0
$