v=-1/39v-2=3v

Solution for v=-1/39v-2=3v equation:

v=-1/39v-2=3v

We move all terms to the left:

v-(-1/39v-2)=0


Domain of the equation: 39v-2)!=0

v∈R


We get rid of parentheses

v+1/39v+2=0

We multiply all the terms by the denominator


v*39v+2*39v+1=0

Wy multiply elements

39v^2+78v+1=0

a = 39; b = 78; c = +1;
Δ = b2-4ac
Δ = 782-4·39·1
Δ = 5928
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5928}=\sqrt{4*1482}=\sqrt{4}*\sqrt{1482}=2\sqrt{1482}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(78)-2\sqrt{1482}}{2*39}=\frac{-78-2\sqrt{1482}}{78}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(78)+2\sqrt{1482}}{2*39}=\frac{-78+2\sqrt{1482}}{78}
$