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

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

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

We move all terms to the left:

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


Domain of the equation: 5v!=0

v!=0/5

v!=0

v∈R



Domain of the equation: 2v!=0

v!=0/2

v!=0

v∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-20v^2)/160v^2+32v/160v^2+240v/160v^2=0

We multiply all the terms by the denominator


(-20v^2)+32v+240v=0

We add all the numbers together, and all the variables

(-20v^2)+272v=0

We get rid of parentheses

-20v^2+272v=0

a = -20; b = 272; c = 0;
Δ = b2-4ac
Δ = 2722-4·(-20)·0
Δ = 73984
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{73984}=272$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(272)-272}{2*-20}=\frac{-544}{-40}
=13+3/5
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(272)+272}{2*-20}=\frac{0}{-40}
=0
$