It's been a while since I studied maths, so hopefully i am using the right terms. I want to solve the following equation for $t$. That is, I want an equation like $t =$ .....
I tried factoring it and whatnot and wound up with it in quadratic equation form. But solving the quadratic equation gave values of $t$ that are impossible for any given $v$. I'm certain I solved the quadratic equation properly, so i can only assume I got to the quadratic equation in an erroneous way. Any help would be greatly appreciated. Cheers.
$\left(\frac{330}{t}\right)^2 = \sqrt{1.36 + \left(1.17 + \frac{v}{t} \right)^2}$
Let $x=1/t$; then the equation can be rewritten as
$$(330x)^2=\sqrt{1.36+(1.17+vx)^2}.$$
Squaring both sides yields
$$(330x)^4=1.36+(1.17+vx)^2,$$
and expanding and rearranging gives us
$$11859210000\cdot x^4-v^2\cdot x^2-2.34v\cdot x-2.7289=0.$$
This is a quartic, not a quadratic equation. There are closed formulas for the solutions, but I suppose numeric approaches are what you're looking for?