[Iridonia]

Hey.

I'm really struggling with this one. In regards to which steps I've taken to solve it on my own, I got nothing but some pathetic attempts to isolate [ S] or play around with the formula. I'm spectacularly bad at this type of chemistry. I've read up on it but I still don't get it.
I'll try to translate it to the best of my ability.

The link between the substrate concentration [ S] and the initial velocity V₀ is given by the following equation:

V₀ = V_max*[ S]/K_m+[ S]

Indicate the amount of [ S] (in relation to K_m) in which V₀ = 66,67% of the maximal velocity.

Thank you

[Borek]

From the sound of it yours is not a problem with chemistry, but with algebra.

Note: shorthand that you used to enter the formula is incorrect, as it suggests second [itex]\left[S\right][/itex] is not part of the denominator. Adding parentheses will make the notation unambiguous.

Start by multiplying both sides by [itex](K_m + \left[S\right])[/itex].

[Babcock_Hall]

@OP,

Borek made a good point about notation.  An alternative way to perform the algebra is to divide both sides by V_max.

[Borek]

An alternative way to perform the algebra is to divide both sides by V_max.

While it is definitely a necessary step it won't help in solving for [itex]\left[S\right][/itex], which is probably the most challenging part of the manipulation.