-5/3v+2/5=-3/5v-3

Solution for -5/3v+2/5=-3/5v-3 equation:

-5/3v+2/5=-3/5v-3

We move all terms to the left:

-5/3v+2/5-(-3/5v-3)=0


Domain of the equation: 3v!=0

v!=0/3

v!=0

v∈R



Domain of the equation: 5v-3)!=0

v∈R


We get rid of parentheses

-5/3v+3/5v+3+2/5=0

We calculate fractions


(-625v)/375v^2+9v/375v^2+6v/375v^2+3=0

We multiply all the terms by the denominator


(-625v)+9v+6v+3*375v^2=0

We add all the numbers together, and all the variables

15v+(-625v)+3*375v^2=0

Wy multiply elements

1125v^2+15v+(-625v)=0

We get rid of parentheses

1125v^2+15v-625v=0

We add all the numbers together, and all the variables

1125v^2-610v=0

a = 1125; b = -610; c = 0;
Δ = b2-4ac
Δ = -6102-4·1125·0
Δ = 372100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{372100}=610$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-610)-610}{2*1125}=\frac{0}{2250}
=0
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-610)+610}{2*1125}=\frac{1220}{2250}
=122/225
$