I'm having a problem in this please i would really appreciate if someone can solve this for me with the formula and everything

 

1- Find the whole number such that four times the number subtracted from three times the square of the number makes 15.

Let n be an integer such that 3n^2 - 4n=15, find n.

 

Can be done in two ways. one you can use the quadratic formula, but better, factor the left and right and conclude something using uniqueness of prime factorization

1.66666666 or -3

(using quad form)

just work through the formula on paper, and you should get that (well I did any way :-S)

I'm having a problem in this please i would really appreciate if someone can solve this for me with the formula and everything

 

1- Find the whole number such that four times the number subtracted from three times the square of the number makes 15.

 

3n2-4n=15

3n2-4n-15=0

 

n=(4(+/-)sqrt(16-4(3)(-15)))/6

 

n=(4(+/-)sqrt(16+180))/6

 

n=(4(+/-)14)/6

 

 

 

n=(2+7)/3 n=3

or

n=(2-7)/3 n=-5/3

In all honesty it is far better to do it with integer factorizations:

 

n(3n-4) = 3*5

 

though in this case you need to consider -3*-5 as an option too.

 

I say this because this techique allows you to solve equations like: find all primes, p such that p+9=n^2 where n is an integer, and we do not even need to consider anything as high faluting as a formula.