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.

Can't you just take the top and set it equal to the bottom (anything divided by itself is one) then solve for R?

Also, at first glance this looks like some differential equations,  but I only vaguely remember this (touched on it in calculus).