I don't understand what I did wrong, please help​

Step-by-step explanation:

Lets start with the easiest part of this question - simply plugging in to get easier equations:

Something that now immedietly pops out is that many of the terms would cancel if we added them together. We get the following results by adding the two equations together:

Now lets look at the other bit of inromation the question gives you -- that the two points are horizontal tangents. Taking the derivative of the standard form of a cubic, we get:

Since the points are both horizontal tangents, y' will be equal to 0 at the points. Thus, plugging in we get:

We again see a simple subtracting opportunity that will cancel out two terms:

Now going back to the equation we got by adding the two equations that we got from simply plugging our points in:

Now that we have b and d, we can now plug them back into our step one and derivative equations in order to get a simple system:

Solving for a and c, we get:

Thus, finally, our answer is:

Attached is desmos, which you can use to check.

1st integer x

2nd integer x+1

3rd integer x+2

4th integer x+3

x+x+1 +x+2+x+3 =74

combine like terms

4x+6 = 74

subtract 6 from each side

4x = 68

x = 17

the integers are 17,18,19,20

show us the triangle so we can answer it