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23 2/3

So basically is there are x sides, there will be x*(x-1)/2 - x diagonals, and if 2x = x*(x-1)/2 - x, then x must equal to 7, septagon. Go on, try it! 

Like so:

That is completely wrong as you made a ton of mistakes in your proof and that you somehow got 5(a+2)(b+2)(c+2)=abc when it is actually a-2, b-2, and c-2.

(1349​,7) and (225​,7).

This should help:

For f(5x+5) to equal 4 we must have 5x+5 = 3,  so x = -2/5.

At x = -2/5 we have y = 1/5 * 4 - 5  or y = -21/5 

So the point (-2/5, -21/5) is on the graph.   (The point can also be expressed as (-0.4, -4.2) )

The PERPINDICULAR line from the origin has a slope of   - 1/m =  -1/2 

  so  this line is  y = - 1/2 x 

   A circle of radius 5 , centered at the origin (  x^2 + y^2 = 5^2 ) 

    Intersects are prpindicular line at   (4.472 , -2.236) 

        NOW....the equation of the line that contains THIS point and has a slope of 2 is 

                     y + 2.236 = 2 ( x - 4.472) 

                   or  y = 2x - 11.18 

This has a y-axis intercept of  - 11.18    and the x intercept is 5.59 

Area of the triangle is 1/2 base * height     

     = 1/2   * 11.18  * 5.59 =  31.25 units^2 

Here is a Desmos graph showing all of this :

We can simplifify this equation first. 

x - y^2 + 8y = 13 + 2y + y^2 - 7y - 14

x+8y=13+2y+2y^2 -7y-14

x+8y=2y+2y^2 -7y -1

x+6y=2y^2 - 7y - 1

x+13y=2y^2-2

x=2y^2-13y-1

Then we can write this into vertex form, try this part yourself! 

If needed, help for this step can be found through MathWay.

Scroll Down for Answer:

Here it is! (13/4, -177/8)

Wondeful thinking BlackjackEd!

However, there is an alternative method:

3X=81 x 5

We could first divide both sides by 3 and get

X=27 x 5

This also gives us 135.