Quick question about a small problem

[Elpinetos]

Homework Statement

In my work I am stuck at this equation:
$840+1.5v^{2.4}-3.6v^{1.4}=0$

I am looking for a quick, easy way to solve this.
Any suggestions? I am kinda tired right now and nothing comes to my mind except maybe Newtons method?

 

[Elpinetos]

Okay, so this equation comes from the derivative of

$s(x)=\frac{600v}{1.4+0.0025*v^{2.4}}$

But Wolfram Alpha tells me the derivative is wrong? Oo
What did I do wrong?

$s'(x)=\frac{600(1.4+0.0025v^{2.4})-600v(0.006v^{1.4})}{(1.4+0.0025*v^{2.4})^{2}}$

$s'(x)=\frac{840+1.5v^{2.4}-3.6v^{1.4}}{(1.4+0.0025*v^{2.4})^{2}}$

 

[Ray Vickson]

Okay, so this equation comes from the derivative of

$s(x)=\frac{600v}{1.4+0.0025*v^{2.4}}$

But Wolfram Alpha tells me the derivative is wrong? Oo
What did I do wrong?

$s'(x)=\frac{600(1.4+0.0025v^{2.4})-600v(0.006v^{1.4})}{(1.4+0.0025*v^{2.4})^{2}}$

$s'(x)=\frac{840+1.5v^{2.4}-3.6v^{1.4}}{(1.4+0.0025*v^{2.4})^{2}}$

$v \times v^{1.4} = v^{2.4}$, not $v^{1.4}$.

 

[Ray Vickson]

Homework Statement

In my work I am stuck at this equation:
$840+1.5v^{2.4}-3.6v^{1.4}=0$

I am looking for a quick, easy way to solve this.
Any suggestions? I am kinda tired right now and nothing comes to my mind except maybe Newtons method?

A simple plot of $840+1.5v^{2.4}-3.6v^{1.4}$ shows that the equation has no positive real roots and hence has no real roots at all.

 

[Elpinetos]

Thanks, I overlooked the v