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

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

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

We move all terms to the left:

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


Domain of the equation: 2v!=0

v!=0/2

v!=0

v∈R



Domain of the equation: 3v-1)!=0

v∈R


We get rid of parentheses

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

We calculate fractions


189v/54v^2+10v/54v^2+(-8v)/54v^2+1=0

We multiply all the terms by the denominator


189v+10v+(-8v)+1*54v^2=0

We add all the numbers together, and all the variables

199v+(-8v)+1*54v^2=0

Wy multiply elements

54v^2+199v+(-8v)=0

We get rid of parentheses

54v^2+199v-8v=0

We add all the numbers together, and all the variables

54v^2+191v=0

a = 54; b = 191; c = 0;
Δ = b2-4ac
Δ = 1912-4·54·0
Δ = 36481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36481}=191$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(191)-191}{2*54}=\frac{-382}{108}
=-3+29/54
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(191)+191}{2*54}=\frac{0}{108}
=0
$