find value of R

here's a problem i was discussing with my teacher, who told me he'd give me extra credit if i could find an answer. i'm starting to think it's mathematically impossible, though.

1.4R-.4 = R^1.4
what is R?

background:
a regular, four-stroke engine (otto cycle) has this formula for efficiency:
1-(1/compression ratio)^K-1
a four-stroke diesel engine has this formula for efficiency:
1-(1/compression ratio)^K-1*[(R^K-1)/(K(R-1))]
so, given identical compression ratios and K values, is there a value of R that will give these two engines the same efficiency? i'm given compression ratio = 7 and K = 1.4. so, for the same efficiency, [(R^K-1)/(K(R-1))] must equal 1, which i transformed to the original equation. i've been looking at it for a couple hours and kind of gotten stuck, maybe someone can give me some further insight.

>>9
what? i've forgotten most of the differential equations i learned. google says the solution is a negative number, a complex number, or the number one. -2.92711 satisfies both versions of the equation, but a negative cut-off ratio is physically impossible, that would mean the volume was greater before combustion. the complex solutions don't really exist, so none of those are possible solutions, right?