Help please with a few quadratics

I have a few problems I have having difficulty at arriving at a solution that fits correctly.

The first one solve the equation:

5x^2 - x - 1 = 0

The second seems to be very difficult for me:

The Function

f (x) = -0.02x^2 + x + 1

moldels the yearly growth of a young redwood tree, f (x), in inches, with x inches of rainfall per year. How many inches of rainfall per year result in maximum tree growth? What is the yearly growth?

The Third Problem:

Solve equation by making an appropriate substitution. When necessary check proposed solutions.

x^-2 + x^-1 - 56 = 0

Fourth Problem:

Express solution to equation in simplified form. Rationalize denominators. Solve equation by the square root property.

(x - 3)^2 = 20

Earboth or Hacker are you around?

A baseball player hits a pop fly into the air. The function

s(t) = - 16t^2 + 64t + 5

When does the baseball reach its maximum height? What is that height?

Okay I have tried several times to come up with this answer as in the book which is

The baseball will reach its maximum height of 69 feet after 2 seconds.

I am really confused once I turn the equation into the vertex.

Please help me. I know you both have different ways of doing them and I have tried both but I am completely missing something here?