Question about quadratic formula/parabolas

The question is:

A parabola has zeros -6 and 2 and y-intercept -9.

a) Write its equation in factored form, expanded form and vertex form.

b)Use the expanded form and the quadratic formula to verify that the zeros are -6 and 2.

First, to write the equation in factored form I substituted y=-9, x=0 to find a.

y=a(x-s)(x-t)

-9=a(0+6)(0-2)

-9=a(-6)(2)

-9=-12a

3/4=a

Which therefore made the equation in factored form:

y=3/4(x+6)(x-2)

And it was therefore in expanded form:

y=3/4x^2+3x-9

However, in checking the zeros of this equation with the quadratic formula,

I could not get -6 and 2 for the zeros.

x=-bħsquare root of b^+4ac/2a

x=-3ħsquare root of 3x3+4(3/4)(-9)/2a

x=-3ħsquare root of 9-27/2a

x=-3ħsquare root of -18 /2a

Already I know that this is wrong.

Please help?

I must email this to my teacher before the end of the week.