3/5v+5/2v=-31/10

Solution for 3/5v+5/2v=-31/10 equation:

3/5v+5/2v=-31/10

We move all terms to the left:

3/5v+5/2v-(-31/10)=0


Domain of the equation: 5v!=0

v!=0/5

v!=0

v∈R



Domain of the equation: 2v!=0

v!=0/2

v!=0

v∈R


We get rid of parentheses

3/5v+5/2v+31/10=0

We calculate fractions


620v^2/100v^2+60v/100v^2+250v/100v^2=0

We multiply all the terms by the denominator


620v^2+60v+250v=0

We add all the numbers together, and all the variables

620v^2+310v=0

a = 620; b = 310; c = 0;
Δ = b2-4ac
Δ = 3102-4·620·0
Δ = 96100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{96100}=310$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(310)-310}{2*620}=\frac{-620}{1240}
=-1/2
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(310)+310}{2*620}=\frac{0}{1240}
=0
$