I think at this point, if you have the units consistent, you can drop them and just go for the numeric solution. Youwill know what are the correct units, for x, from the fact that it must agree with the units for V/b (so that that denominator has consistent units).

The units are in need of minor conversions to like units, but the fundamental units are all the same (m^3 -> dm^3, for example), but the fundamental structure of the equation is functionally correct (it's pulled from a text book). If I remember right, I did try preconverting everything into matching units at one point, but was stymied by "W|A does not understand your input"more than likely because the input string remains half as long as my arm.

Converting everything to like units gives these: p=x (-a x/v^2 + r t/(v-b x)) a=0.2420((atm*dm^6)/(mol^2)) b=((2.6510^-2)*((dm^3)/mol) P=(1.0*atm) R=((8.20573610^-5)*((m^3atm)/(k * mol))) T=298.2*K V=(113097*dm^3)]

*edited because there was a minor error in the text. Second edit: kmol should have been K * mol

You can get the numerical values as already indicated (dropping all units, that is). Presumably any part of the input that gives compatibility conditions on the units will show what they must be. For example, the denominator V-b*x shows that x must have same units as V/b.

All this requires that the input be preprocessed so that units are all expressed in the same system e.g. CGS. And that the equation be dimentionally correct to begin with. If you want to actually demonstrate that (e.g. you want to show there was no error in the input) then I suspect Alpha will not be the tool of choice. Not sure about Alpha Pro though.

One trick to get around some limitations of WolframAlpha is to let it do part of your calculation, scrape the result and use that to build a final calculation that gives you the answer you really want.

Go to WolframAlpha and paste

a=0.2420; b=2.6510^-2; r=8.20573610^-5; v=113.097; t=298.2; x(-a x/v^2+r t/(v-b x))

Gently slide the mouse over the result until you see "Copyable plaintext" and click and scrape

(0.05633 x)/(794.823-x)-0.0000189197 x^2

Then give WolframAlpha input

p=1;solve for x: p= (0.05633 x)/(794.823-x)-0.0000189197 x^2

tle last part of which is what you scraped from above and then get

x= -52854.9

x= 0

x=794.768

Or just quit fighting this sillyness and let Excel give you the answer

aye, I did this at one point and got probably that exact output. What i'm looking to do is have it CALCULATE that equation given the following definitions for each of the variables: a=0.2420((atmdm^6)/(mol^2)) b=((2.6510^-2)((dm^3)/mol) P=(1.0atm) R=((8.20573610^-5)((m^3atm)/(kmol))) T=298.2*K V=(113.097m^3)] specifically WITH the units going along for the ride. As you can tell from the solution above, running this by hand is a NIGHTMARE. I need a CAS to chew this out.