1/2v+8=3-1/3v

Solution for 1/2v+8=3-1/3v equation:

1/2v+8=3-1/3v

We move all terms to the left:

1/2v+8-(3-1/3v)=0


Domain of the equation: 2v!=0

v!=0/2

v!=0

v∈R



Domain of the equation: 3v)!=0

v!=0/1

v!=0

v∈R


We add all the numbers together, and all the variables

1/2v-(-1/3v+3)+8=0

We get rid of parentheses

1/2v+1/3v-3+8=0

We calculate fractions


3v/6v^2+2v/6v^2-3+8=0

We add all the numbers together, and all the variables

3v/6v^2+2v/6v^2+5=0

We multiply all the terms by the denominator


3v+2v+5*6v^2=0

We add all the numbers together, and all the variables

5v+5*6v^2=0

Wy multiply elements

30v^2+5v=0

a = 30; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·30·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*30}=\frac{-10}{60}
=-1/6
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*30}=\frac{0}{60}
=0
$