3/2v-7/2=-1/5v-4

Solution for 3/2v-7/2=-1/5v-4 equation:

3/2v-7/2=-1/5v-4

We move all terms to the left:

3/2v-7/2-(-1/5v-4)=0


Domain of the equation: 2v!=0

v!=0/2

v!=0

v∈R



Domain of the equation: 5v-4)!=0

v∈R


We get rid of parentheses

3/2v+1/5v+4-7/2=0

We calculate fractions


15v/40v^2+8v/40v^2+(-35v)/40v^2+4=0

We multiply all the terms by the denominator


15v+8v+(-35v)+4*40v^2=0

We add all the numbers together, and all the variables

23v+(-35v)+4*40v^2=0

Wy multiply elements

160v^2+23v+(-35v)=0

We get rid of parentheses

160v^2+23v-35v=0

We add all the numbers together, and all the variables

160v^2-12v=0

a = 160; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·160·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*160}=\frac{0}{320}
=0
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*160}=\frac{24}{320}
=3/40
$