To solve the first equation 7x^2 - 3x - 4 = 0:

We can factor the equation by looking for two numbers that multiply to -28 (the product of 7 and -4) and add up to -3. The numbers are -7 and 4.

Therefore, we can rewrite the equation as:

7x^2 - 7x + 4x - 4 = 0
7x(x - 1) + 4(x - 1) = 0
(7x + 4)(x - 1) = 0

Setting each factor to zero:
7x + 4 = 0
7x = -4
x = -4/7

x - 1 = 0
x = 1

So, the solutions to the first equation are x = -4/7 and x = 1.

To solve the second equation 9x^2 + (9 - √2)x - √2 = 0:

We can't directly factor this equation, so we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

a = 9, b = 9 - √2, c = -√2

Substitute the values in:

x = (-(9 - √2) ± √((9 - √2)^2 - 49-√2)) / 2*9
x = (-(9 - √2) ± √(81 - 18√2 + 2 - 72√2)) / 18
x = (-(9 - √2) ± √(83 - 90√2)) / 18
x = (-(9 - √2) ± √(83 - 90√2)) / 18

So, the solutions to the second equation are x = (9 - √2 ± √(83 - 90√2)) / 18.