1/8v=20v=

Solution for 1/8v=20v= equation:

1/8v=20v=

We move all terms to the left:

1/8v-(20v)=0


Domain of the equation: 8v!=0

v!=0/8

v!=0

v∈R


We add all the numbers together, and all the variables

-20v+1/8v=0

We multiply all the terms by the denominator


-20v*8v+1=0

Wy multiply elements

-160v^2+1=0

a = -160; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-160)·1
Δ = 640
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:

$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{10}}{2*-160}=\frac{0-8\sqrt{10}}{-320}
=-\frac{8\sqrt{10}}{-320}
=-\frac{\sqrt{10}}{-40}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{10}}{2*-160}=\frac{0+8\sqrt{10}}{-320}
=\frac{8\sqrt{10}}{-320}
=\frac{\sqrt{10}}{-40}
$