v=2v/3v+15

Solution for v=2v/3v+15 equation:

v=2v/3v+15

We move all terms to the left:

v-(2v/3v+15)=0


Domain of the equation: 3v+15)!=0

v∈R


We get rid of parentheses

v-2v/3v-15=0

We multiply all the terms by the denominator


v*3v-2v-15*3v=0

We add all the numbers together, and all the variables

-2v+v*3v-15*3v=0

Wy multiply elements

3v^2-2v-45v=0

We add all the numbers together, and all the variables

3v^2-47v=0

a = 3; b = -47; c = 0;
Δ = b2-4ac
Δ = -472-4·3·0
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-47)-47}{2*3}=\frac{0}{6}
=0
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+47}{2*3}=\frac{94}{6}
=15+2/3
$