16.5=v2/64

Solution for 16.5=v2/64 equation:

16.5=v2/64

We move all terms to the left:

16.5-(v2/64)=0

We add all the numbers together, and all the variables

-(+v2/64)+16.5=0

We get rid of parentheses

-v2/64+16.5=0

We multiply all the terms by the denominator


-v2+(16.5)*64=0

We add all the numbers together, and all the variables

-1v^2+1056=0

a = -1; b = 0; c = +1056;
Δ = b2-4ac
Δ = 02-4·(-1)·1056
Δ = 4224
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:

$\sqrt{\Delta}=\sqrt{4224}=\sqrt{64*66}=\sqrt{64}*\sqrt{66}=8\sqrt{66}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{66}}{2*-1}=\frac{0-8\sqrt{66}}{-2}
=-\frac{8\sqrt{66}}{-2}
=-\frac{4\sqrt{66}}{-1}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{66}}{2*-1}=\frac{0+8\sqrt{66}}{-2}
=\frac{8\sqrt{66}}{-2}
=\frac{4\sqrt{66}}{-1}
$