You should first write the equation with a 0 on the right:
x³-5x-34 = 0, for it's easier to tell which is closer to 0
than it is to tell which is closer to 34.

When you get a POSITIVE answer, then the next time choose
a value between what you tried to get that POSITIVE answer,
and what you tried the last time you got a NEGATIVE answer.
And vice-versa. 

We substitute 3: 3³-5(3)-34 = -22
We substitute 4: 4³-5(4)-34 = 10

We substitute a number between 3 and 4
with 1 decimal place that is close as possible
to halfway between them.

We substitute 3.5: 3.5³-5(3.5)-34 = -8.625
That's a NEGATIVE number. 

So now we know that the solution is between 3.5 and 
what we substituted the last time we got a POSITIVE 
number, which was when we substituted 4 and got 10.

We substitute a number between 3.5 and 4
with 1 decimal place that is close as possible
to halfway between them.

So we substitute 3.7  (we could substitute 3.8, if we like,
since it's just as close to halfway between 3.5 and 4 as 3.7)

We substitute 3.7: 3.7³-5(3.7)-34 = -1.847

That's another NEGATIVE number.

So now we know that the solution is between 3.7 and 
what we substituted the last time we got a POSITIVE 
number, which was when we substituted 4 and got 10.

We substitute a number between 3.7 and 4
with 1 decimal place that is close as possible
to halfway between them.

So we substitute 3.8  (we could substitute 3.9, if we like)

We substitute 3.8: 3.8³-5(3.8)-34 = 1.842

That's a POSITIVE number.

So now we know that the solution is between 3.8 and 
what we substituted the last time we got a NEGATIVE 
number, which was when we substituted 3.7 and got -1.847.

So the solution is between 3.7 and 3.8, and since
1.842 is closer to 0 than -1.847, the solution
correct to 1 decimal place is 3.8.

Edwin