# Diagonals

What x-gon has 54 diagonals?

Result

x =  12

#### Solution:

$\ \\ -0.5n^2 +1.5n +54=0 \ \\ 0.5n^2 -1.5n -54=0 \ \\ \ \\ a=0.5; b=-1.5; c=-54 \ \\ D=b^2 - 4ac=1.5^2 - 4\cdot 0.5 \cdot (-54)=110.25 \ \\ D>0 \ \\ \ \\ n_{1,2}=\dfrac{ -b \pm \sqrt{ D } }{ 2a }=\dfrac{ 1.5 \pm \sqrt{ 110.25 } }{ 1 } \ \\ n_{1,2}=1.5 \pm 10.5 \ \\ n_{1}=12 \ \\ n_{2}=-9 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ 0.5 (n -12) (n +9)=0 \ \\ \ \\ x>0 \ \\ \ \\ x=n_{1}=12$

Checkout calculation with our calculator of quadratic equations.

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Be the first to comment!

Tips to related online calculators
Looking for help with calculating roots of a quadratic equation?
Would you like to compute count of combinations?

## Next similar math problems:

1. Combinations
How many elements can form six times more combinations fourth class than combination of the second class?
2. Combinations
From how many elements we can create 990 combinations 2nd class without repeating?
3. 2nd class combinations
From how many elements you can create 4560 combinations of the second class?
4. One green
In the container are 45 white and 15 balls. We randomly select 5 balls. What is the probability that it will be a maximum one green?
Find the roots of the quadratic equation: 3x2-4x + (-4) = 0.
6. Equation
Equation ? has one root x1 = 8. Determine the coefficient b and the second root x2.
7. Discriminant
Determine the discriminant of the equation: ?
8. Roots
Determine the quadratic equation absolute coefficient q, that the equation has a real double root and the root x calculate: ?
9. Theorem prove
We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
10. Fish tank
A fish tank at a pet store has 8 zebra fish. In how many different ways can George choose 2 zebra fish to buy?
11. Trinity
How many different triads can be selected from the group 43 students?
12. Calculation of CN
Calculate: ?
13. Examination
The class is 21 students. How many ways can choose two to examination?
14. Division
Division has 18 members: 10 girls and 6 boys, 2 leaders. How many different patrols can be created, if one patrol is 2 boys, 3 girls and 1 leader?
15. A student
A student is to answer 8 out of 10 questions on the exam. a) find the number n of ways the student can choose 8 out of 10 questions b) find n if the student must answer the first three questions c) How many if he must answer at least 4 of the first 5 qu
16. Chords
How many 4-tones chords (chord = at the same time sounding different tones) is possible to play within 7 tones?
17. Confectionery
The village markets have 5 kinds of sweets, one weighs 31 grams. How many different ways a customer can buy 1.519 kg sweets.