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

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

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

We move all terms to the left:

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


Domain of the equation: 2v!=0

v!=0/2

v!=0

v∈R



Domain of the equation: 5v-2)!=0

v∈R


We get rid of parentheses

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

We calculate fractions


(-15v)/40v^2+(-32v)/40v^2+(-25v)/40v^2+2=0

We multiply all the terms by the denominator


(-15v)+(-32v)+(-25v)+2*40v^2=0

Wy multiply elements

80v^2+(-15v)+(-32v)+(-25v)=0

We get rid of parentheses

80v^2-15v-32v-25v=0

We add all the numbers together, and all the variables

80v^2-72v=0

a = 80; b = -72; c = 0;
Δ = b2-4ac
Δ = -722-4·80·0
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-72}{2*80}=\frac{0}{160}
=0
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+72}{2*80}=\frac{144}{160}
=9/10
$