Question 47642
1/1.33 = 1/(R1-6) + 1/R1
I'm going to replace R1 by "x" as it is easier to type.
1/1.33 = 1/(x-6) + 1/x
1/1.33 = [x+x-6]/[x(x-6)]
1/1.33 = [2x-6)]/[x^2-6x]
Cross-multiply to get;
x^2-6x=2.66x-7.98
x^2-8.66x+7.98=0

x=[8.66+sqrt(8.66^2-4(7.98)]/2 or x=[8.66-sqrt(8.66^2-4(7.98)]/2

x=[8.66+sqrt43.0756]/2 or x=[8.66-sqrt(43.0756)]/2
Reverting now to x=R1 you get:
R1=7.61160022... or R1=2.09679956...
 
Only R1=7.61160022... is a valid answer
The other is an extraneous result of the way the
quadratic equation was formed.  That means the 
2nd answer is valid for the quadratic equation but
not for your original equation.
Cheers,
Stan H.