After correcting minor syntax errors, the meaning OP intends is something like...
Now, let's use the formula above so that [+we can] achieve
the further results
...but he wants to express this in a "fancier" (more formal) way. In which context it's worth noting that "imperative" let's is a relatively informal construction in the above.
Possible alternatives include:
1: Having shown [you] the formula, I will [now] use it [in some practical examples]
2: The formula having been shown, we can use it [to solve a problem]
(where the text in brackets is whatever you intend to talk about next).
The second form above isn't very "natural". I've only really included it to show how the passive verb form works differently in such contexts. Note that in #1, the "subject" of having can only be the first noun after the comma (I)1. But because #2 is a passive usage (where that "subject" is unspecified, unknown), it's fine to follow it with either I can use it OR we will use it.
That's to say, with version #2, the current speaker may be the person who showed the results earlier, but it's always possible that was done by a previous speaker. But it's a bit meaningless to talk about "ambiguity" here, since obviously the audience know perfectly well who just showed them the formula without having to be explicitly told!
1 Note that the construction having [verbed] [subject] [verb] is a stylistically reduced version of [subject] having [verbed] [subject] [verb]. So...
having eaten, John went to bed
...is semantically / syntactically equivalent to...
John having eaten, he went to bed
(for stylistic reasons, we wouldn't usually repeat John, or start with He and switch to John after the comma; but they're perfectly "valid" forms).