6/5v+8/v=1

Solution for 6/5v+8/v=1 equation:

6/5v+8/v=1

We move all terms to the left:

6/5v+8/v-(1)=0


Domain of the equation: 5v!=0

v!=0/5

v!=0

v∈R



Domain of the equation: v!=0

v∈R


We calculate fractions


6v/5v^2+40v/5v^2-1=0

We multiply all the terms by the denominator


6v+40v-1*5v^2=0

We add all the numbers together, and all the variables

46v-1*5v^2=0

Wy multiply elements

-5v^2+46v=0

a = -5; b = 46; c = 0;
Δ = b2-4ac
Δ = 462-4·(-5)·0
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-46}{2*-5}=\frac{-92}{-10}
=9+1/5
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+46}{2*-5}=\frac{0}{-10}
=0
$