1) 0.7x - 1.4x^2 = 0

To solve this quadratic equation, we need to set it equal to zero and factor out an x:

-1.4x^2 + 0.7x = 0

Now, we can factor out an x:

x(-1.4x + 0.7) = 0

Now, we set each factor equal to zero:

x = 0

and

-1.4x + 0.7 = 0
-1.4x = -0.7
x = -0.7 / -1.4
x = 0.5

Therefore, the solutions to the equation 0.7x - 1.4x^2 = 0 are x = 0 and x = 0.5.

2) 1/7x + 3 1/7x^2 = 0

To solve this quadratic equation, we first need to find a common denominator:

1/7x + 3 * 1/7x^2 = 0
(1x + 21) / 7x^2 = 0

Now, we set the numerator equal to zero:

1x + 21 = 0
1x = -21
x = -21/1
x = -21

Therefore, the solution to the equation 1/7x + 3 1/7x^2 = 0 is x = -21.