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

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

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

We move all terms to the left:

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


Domain of the equation: 2v!=0

v!=0/2

v!=0

v∈R



Domain of the equation: 4v-3)!=0

v∈R


We get rid of parentheses

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

We calculate fractions


(-32v^2)/72v^2+(-108v)/72v^2+(-90v)/72v^2+3=0

We multiply all the terms by the denominator


(-32v^2)+(-108v)+(-90v)+3*72v^2=0

Wy multiply elements

(-32v^2)+216v^2+(-108v)+(-90v)=0

We get rid of parentheses

-32v^2+216v^2-108v-90v=0

We add all the numbers together, and all the variables

184v^2-198v=0

a = 184; b = -198; c = 0;
Δ = b2-4ac
Δ = -1982-4·184·0
Δ = 39204
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{39204}=198$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-198)-198}{2*184}=\frac{0}{368}
=0
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-198)+198}{2*184}=\frac{396}{368}
=1+7/92
$