For the following question, have i solved properly so far?

Question

Find the exact roots (algebraically) for the cubic equation x^3-5x^2-7x+51=0 (include a list of all possible integral roots) Support your findings with the graph of an appropriate cubic polynomial, clearly explainging how this graph confirms your algebraic solution:
This is my solution :
x^3-5x^2-7x+51=0
f(-3)=(-3)^3-5(-3)^2-7(-3)+51
=0 therefor (x+3) is a factor

(x^3-5x^2-7x+51) divided by (x+3)
= x^2-8x+17 therefor x^2-8x+17=0 is a factor...
so the following roots are x=-3 and x=+-squareroot -4 all over 2

Answer 1

so the following roots are x=-3 and
x= 8 +/- squareroot -4 all over 2
= 4 +/- i

Answer 2

I agree except you left out the "-b" part of the quadratic formula so it should be 8 +- sqrt -4 all over 2