Help understanding the quadratic equation

Question

I understand how to solve these by factoring them but I am having trouble understanding how to use the quadratic equation. If you know how to solve a quadratic equation please help me.  We are not allowed to solve them by factoring them. Thanks!

1. x^2 - 4x - 5 = 0

2. z^2 - 2z - 15 = 0

3. y^2 = 2y + 3

4. r^2 = 5 - 4r

Once again, thanks for the help!

Answer 1

if the quadratic eqn is ax^2 + bx+c = 0 you can use the formula -a +/- sqrt(b^2-4ac) / (2a)

in your case, all can be factored

1. (x-5)(x+1) = 0

2. (z-5)(z+3) = 0

3. (y-3)(y+1) = 0

4. (r+5)(r-1) = 0