3/2v+9/2-11/3v=23/8

Solution for 3/2v+9/2-11/3v=23/8 equation:

3/2v+9/2-11/3v=23/8

We move all terms to the left:

3/2v+9/2-11/3v-(23/8)=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-(+23/8)=0

We get rid of parentheses

3/2v-11/3v+9/2-23/8=0

We calculate fractions


(-828v^2)/192v^2+576v/192v^2+(-704v)/192v^2+1728v/192v^2=0

We multiply all the terms by the denominator


(-828v^2)+576v+(-704v)+1728v=0

We add all the numbers together, and all the variables

(-828v^2)+2304v+(-704v)=0

We get rid of parentheses

-828v^2+2304v-704v=0

We add all the numbers together, and all the variables

-828v^2+1600v=0

a = -828; b = 1600; c = 0;
Δ = b2-4ac
Δ = 16002-4·(-828)·0
Δ = 2560000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2560000}=1600$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1600)-1600}{2*-828}=\frac{-3200}{-1656}
=1+193/207
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1600)+1600}{2*-828}=\frac{0}{-1656}
=0
$