8/3v+5/v=1

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

8/3v+5/v=1

We move all terms to the left:

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


Domain of the equation: 3v!=0

v!=0/3

v!=0

v∈R



Domain of the equation: v!=0

v∈R


We calculate fractions


8v/3v^2+15v/3v^2-1=0

We multiply all the terms by the denominator


8v+15v-1*3v^2=0

We add all the numbers together, and all the variables

23v-1*3v^2=0

Wy multiply elements

-3v^2+23v=0

a = -3; b = 23; c = 0;
Δ = b2-4ac
Δ = 232-4·(-3)·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-23}{2*-3}=\frac{-46}{-6}
=7+2/3
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+23}{2*-3}=\frac{0}{-6}
=0
$