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

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

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

We move all terms to the left:

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


Domain of the equation: 3v!=0

v!=0/3

v!=0

v∈R



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

v∈R


We get rid of parentheses

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

We calculate fractions


25v/135v^2+81v/135v^2+(-20v)/135v^2+7=0

We multiply all the terms by the denominator


25v+81v+(-20v)+7*135v^2=0

We add all the numbers together, and all the variables

106v+(-20v)+7*135v^2=0

Wy multiply elements

945v^2+106v+(-20v)=0

We get rid of parentheses

945v^2+106v-20v=0

We add all the numbers together, and all the variables

945v^2+86v=0

a = 945; b = 86; c = 0;
Δ = b2-4ac
Δ = 862-4·945·0
Δ = 7396
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7396}=86$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(86)-86}{2*945}=\frac{-172}{1890}
=-86/945
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(86)+86}{2*945}=\frac{0}{1890}
=0
$