3/2v+9/2-11/3v=7/24

Solution for 3/2v+9/2-11/3v=7/24 equation:

3/2v+9/2-11/3v=7/24

We move all terms to the left:

3/2v+9/2-11/3v-(7/24)=0


Domain of the equation: 2v!=0

v!=0/2

v!=0

v∈R



Domain of the equation: 3v!=0

v!=0/3

v!=0

v∈R


We add all the numbers together, and all the variables

3/2v-11/3v+9/2-(+7/24)=0

We get rid of parentheses

3/2v-11/3v+9/2-7/24=0

We calculate fractions


(-252v^2)/576v^2+432v/576v^2+(-2112v)/576v^2+1296v/576v^2=0

We multiply all the terms by the denominator


(-252v^2)+432v+(-2112v)+1296v=0

We add all the numbers together, and all the variables

(-252v^2)+1728v+(-2112v)=0

We get rid of parentheses

-252v^2+1728v-2112v=0

We add all the numbers together, and all the variables

-252v^2-384v=0

a = -252; b = -384; c = 0;
Δ = b2-4ac
Δ = -3842-4·(-252)·0
Δ = 147456
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{147456}=384$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-384)-384}{2*-252}=\frac{0}{-504}
=0
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-384)+384}{2*-252}=\frac{768}{-504}
=-1+11/21
$