v^2/5=64

Solution for v^2/5=64 equation:

v^2/5=64

We move all terms to the left:

v^2/5-(64)=0

We multiply all the terms by the denominator


v^2-64*5=0

We add all the numbers together, and all the variables

v^2-320=0

a = 1; b = 0; c = -320;
Δ = b2-4ac
Δ = 02-4·1·(-320)
Δ = 1280
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:

$\sqrt{\Delta}=\sqrt{1280}=\sqrt{256*5}=\sqrt{256}*\sqrt{5}=16\sqrt{5}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{5}}{2*1}=\frac{0-16\sqrt{5}}{2}
=-\frac{16\sqrt{5}}{2}
=-8\sqrt{5}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{5}}{2*1}=\frac{0+16\sqrt{5}}{2}
=\frac{16\sqrt{5}}{2}
=8\sqrt{5}
$