v=530/v

Solution for v=530/v equation:

v=530/v

We move all terms to the left:

v-(530/v)=0


Domain of the equation: v)!=0

v!=0/1

v!=0

v∈R


We add all the numbers together, and all the variables

v-(+530/v)=0

We get rid of parentheses

v-530/v=0

We multiply all the terms by the denominator


v*v-530=0

Wy multiply elements

v^2-530=0

a = 1; b = 0; c = -530;
Δ = b2-4ac
Δ = 02-4·1·(-530)
Δ = 2120
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:

$\sqrt{\Delta}=\sqrt{2120}=\sqrt{4*530}=\sqrt{4}*\sqrt{530}=2\sqrt{530}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{530}}{2*1}=\frac{0-2\sqrt{530}}{2}
=-\frac{2\sqrt{530}}{2}
=-\sqrt{530}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{530}}{2*1}=\frac{0+2\sqrt{530}}{2}
=\frac{2\sqrt{530}}{2}
=\sqrt{530}
$