-5/2v-1/6=2/3v-5

Solution for -5/2v-1/6=2/3v-5 equation:

-5/2v-1/6=2/3v-5

We move all terms to the left:

-5/2v-1/6-(2/3v-5)=0


Domain of the equation: 2v!=0

v!=0/2

v!=0

v∈R



Domain of the equation: 3v-5)!=0

v∈R


We get rid of parentheses

-5/2v-2/3v+5-1/6=0

We calculate fractions


(-18v^2)/216v^2+(-540v)/216v^2+(-144v)/216v^2+5=0

We multiply all the terms by the denominator


(-18v^2)+(-540v)+(-144v)+5*216v^2=0

Wy multiply elements

(-18v^2)+1080v^2+(-540v)+(-144v)=0

We get rid of parentheses

-18v^2+1080v^2-540v-144v=0

We add all the numbers together, and all the variables

1062v^2-684v=0

a = 1062; b = -684; c = 0;
Δ = b2-4ac
Δ = -6842-4·1062·0
Δ = 467856
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{467856}=684$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-684)-684}{2*1062}=\frac{0}{2124}
=0
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-684)+684}{2*1062}=\frac{1368}{2124}
=38/59
$