25/v=v+9/v

Solution for 25/v=v+9/v equation:

25/v=v+9/v

We move all terms to the left:

25/v-(v+9/v)=0


Domain of the equation: v!=0

v∈R



Domain of the equation: v)!=0

v!=0/1

v!=0

v∈R


We add all the numbers together, and all the variables

25/v-(+v+9/v)=0

We get rid of parentheses

25/v-v-9/v=0

We multiply all the terms by the denominator


-v*v+25-9=0

We add all the numbers together, and all the variables

-v*v+16=0

Wy multiply elements

-1v^2+16=0

a = -1; b = 0; c = +16;
Δ = b2-4ac
Δ = 02-4·(-1)·16
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8}{2*-1}=\frac{-8}{-2}
=+4
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8}{2*-1}=\frac{8}{-2}
=-4
$