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

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

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

We move all terms to the left:

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


Domain of the equation: 4)v!=0

v!=0/1

v!=0

v∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

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

We calculate fractions


-5v^2+()/()+()/()=0

We add all the numbers together, and all the variables

-5v^2+2=0

a = -5; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-5)·2
Δ = 40
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{10}}{2*-5}=\frac{0-2\sqrt{10}}{-10}
=-\frac{2\sqrt{10}}{-10}
=-\frac{\sqrt{10}}{-5}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{10}}{2*-5}=\frac{0+2\sqrt{10}}{-10}
=\frac{2\sqrt{10}}{-10}
=\frac{\sqrt{10}}{-5}
$