14/3v+3/2v=-74/7

Solution for 14/3v+3/2v=-74/7 equation:

14/3v+3/2v=-74/7

We move all terms to the left:

14/3v+3/2v-(-74/7)=0


Domain of the equation: 3v!=0

v!=0/3

v!=0

v∈R



Domain of the equation: 2v!=0

v!=0/2

v!=0

v∈R


We get rid of parentheses

14/3v+3/2v+74/7=0

We calculate fractions


888v^2/294v^2+1372v/294v^2+441v/294v^2=0

We multiply all the terms by the denominator


888v^2+1372v+441v=0

We add all the numbers together, and all the variables

888v^2+1813v=0

a = 888; b = 1813; c = 0;
Δ = b2-4ac
Δ = 18132-4·888·0
Δ = 3286969
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3286969}=1813$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1813)-1813}{2*888}=\frac{-3626}{1776}
=-2+1/24
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1813)+1813}{2*888}=\frac{0}{1776}
=0
$