3n^2-5n-6=9 help please!

3n^2 -5n -6 = 9  This is a quadratic Equation.

3n^2 -5n -15 = 0

It is solved with the Quadratic Formula:

n = [-b +-sqr root (b^2 - 4ac)] / 2a

a = 3

b = -5

c= -15

n = [--5 +- sqr root(25 -4*3*-15)] / 6

n = [5 +- sqr root (25 + 180) / 6

n = [5 +-sqr root (205) ] / 6

n = 5 + 14.3178210633 / 6

n1 = 19.3178210633 / 6

n1= 3.2196368439

n2= 5 - 14.3178210633 / 6

n2 = -9.3178210633 / 6

n2 = -1.5529701772

Step-by-step explanation:

n = 5/6 ±√(205/36)

n ≈ -1.55297, 3.21964

Step-by-step explanation:

3n² - 5n - 6 = 9

3(n² - (5/3)n - 2) = 9

 (n² - (5/3)n - 2) = 9/3

 (n² - (5/3)n     ) = 3 + 2

 (n² - (5/3)n + (5/6)²) = 5 + (5/6)²

             (the added term will always be the square of b/2)

 (n -  (5/6))² = 5 + 25/36

  n -  5/6 = ±√(205/36)

  n = 5/6 ±√(205/36)

n ≈ -1.55297, 3.21964

See explanation below.

Step-by-step explanation:

Part A:

(i). They both correct because they could have a third degree polynomial that crosses the x-axis 3 times.

(ii). To find the zero's of the first one, set function equal to zero and use zero factor principle given as:

So, we have: