These equations can be solved by factoring, completing the square, or using the quadratic formula. Here are the solutions for each of the given equations:

1) x^2-3x-2=0
(x-2)(x+1)=0
x=2 or x=-1

2) x^2+x-12=0
(x+4)(x-3)=0
x=-4 or x=3

3) x^2-2x-35=0
(x-7)(x+5)=0
x=7 or x=-5

4) x^2+5x-4=0
(x+4)(x-1)=0
x=-4 or x=1

5) x^2-2x-35=0
(x-7)(x+5)=0
x=7 or x=-5

6) x^2+5x-36=0
(x+9)(x-4)=0
x=-9 or x=4

7) x^2+5+14=0
This equation seems to be written incorrectly. It should be:
x^2+5x+14=0
This equation does not factor nicely and can be solved using the quadratic formula:
x = (-5 ± √(5^2 - 4114)) / 2
x ≈ -0.65 or x ≈ -4.35

8) x^2+16x+55=0
(x+11)(x+5)=0
x=-11 or x=-5

9) x^2-4x-77=0
(x-11)(x+7)=0
x=11 or x=-7

10) x^2+20x+91=0
(x+13)(x+7)=0
x=-13 or x=-7

11) x^2-20x+91=0
(x-13)(x-7)=0
x=13 or x=7

12) x^2-18x+45=0
(x-15)(x-3)=0
x=15 or x=3