3/2v-1/2=-7/5v-2

Solution for 3/2v-1/2=-7/5v-2 equation:

3/2v-1/2=-7/5v-2

We move all terms to the left:

3/2v-1/2-(-7/5v-2)=0


Domain of the equation: 2v!=0

v!=0/2

v!=0

v∈R



Domain of the equation: 5v-2)!=0

v∈R


We get rid of parentheses

3/2v+7/5v+2-1/2=0

We calculate fractions


15v/40v^2+56v/40v^2+(-5v)/40v^2+2=0

We multiply all the terms by the denominator


15v+56v+(-5v)+2*40v^2=0

We add all the numbers together, and all the variables

71v+(-5v)+2*40v^2=0

Wy multiply elements

80v^2+71v+(-5v)=0

We get rid of parentheses

80v^2+71v-5v=0

We add all the numbers together, and all the variables

80v^2+66v=0

a = 80; b = 66; c = 0;
Δ = b2-4ac
Δ = 662-4·80·0
Δ = 4356
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4356}=66$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(66)-66}{2*80}=\frac{-132}{160}
=-33/40
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(66)+66}{2*80}=\frac{0}{160}
=0
$