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

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

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

We move all terms to the left:

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


Domain of the equation: 2v!=0

v!=0/2

v!=0

v∈R



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

v∈R


We get rid of parentheses

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

We calculate fractions


(-36v^2)/150v^2+(-225v)/150v^2+(-50v)/150v^2-4=0

We multiply all the terms by the denominator


(-36v^2)+(-225v)+(-50v)-4*150v^2=0

Wy multiply elements

(-36v^2)-600v^2+(-225v)+(-50v)=0

We get rid of parentheses

-36v^2-600v^2-225v-50v=0

We add all the numbers together, and all the variables

-636v^2-275v=0

a = -636; b = -275; c = 0;
Δ = b2-4ac
Δ = -2752-4·(-636)·0
Δ = 75625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{75625}=275$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-275)-275}{2*-636}=\frac{0}{-1272}
=0
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-275)+275}{2*-636}=\frac{550}{-1272}
=-275/636
$