11/5v-9=12/v

Solution for 11/5v-9=12/v equation:

11/5v-9=12/v

We move all terms to the left:

11/5v-9-(12/v)=0


Domain of the equation: 5v!=0

v!=0/5

v!=0

v∈R



Domain of the equation: v)!=0

v!=0/1

v!=0

v∈R


We add all the numbers together, and all the variables

11/5v-(+12/v)-9=0

We get rid of parentheses

11/5v-12/v-9=0

We calculate fractions


11v/5v^2+(-60v)/5v^2-9=0

We multiply all the terms by the denominator


11v+(-60v)-9*5v^2=0

Wy multiply elements

-45v^2+11v+(-60v)=0

We get rid of parentheses

-45v^2+11v-60v=0

We add all the numbers together, and all the variables

-45v^2-49v=0

a = -45; b = -49; c = 0;
Δ = b2-4ac
Δ = -492-4·(-45)·0
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-49)-49}{2*-45}=\frac{0}{-90}
=0
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-49)+49}{2*-45}=\frac{98}{-90}
=-1+4/45
$