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

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

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

We move all terms to the left:

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


Domain of the equation: 2v!=0

v!=0/2

v!=0

v∈R



Domain of the equation: 5v-7)!=0

v∈R


We get rid of parentheses

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

We calculate fractions


25v/40v^2+8v/40v^2+(-15v)/40v^2+7=0

We multiply all the terms by the denominator


25v+8v+(-15v)+7*40v^2=0

We add all the numbers together, and all the variables

33v+(-15v)+7*40v^2=0

Wy multiply elements

280v^2+33v+(-15v)=0

We get rid of parentheses

280v^2+33v-15v=0

We add all the numbers together, and all the variables

280v^2+18v=0

a = 280; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·280·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*280}=\frac{-36}{560}
=-9/140
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*280}=\frac{0}{560}
=0
$