To solve the equations, let's simplify each equation step by step:

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

To get rid of the fractions, we can multiply every term by the least common denominator (LCD), which is 42:

(42)(3/7x) + (42)(1/3) = (42)(1/2)

Simplifying:

(18/7)x + 14 = 21

Subtracting 14 from both sides:

(18/7)x = 7

To isolate x, we can multiply both sides by the reciprocal of (18/7), which is (7/18):

(7/18)(18/7)x = (7/18)(7)

Simplifying:

x = 49/18

Therefore, the solution to the first equation is x = 49/18.

2) -11/12 - (2/5)x = -3/4

To simplify, we can first distribute the negative sign:

-11/12 - 2/5x = -3/4

To get rid of the fractions, we can multiply every term by the LCD, which is 60:

(60)(-11/12) - (60)(2/5x) = (60)(-3/4)

Simplifying:

-55 - 24x = -45

Adding 55 to both sides:

-24x = 10

Dividing both sides by -24:

x = -10/24

Simplifying the fraction:

x = -5/12

Therefore, the solution to the second equation is x = -5/12.

3) (2/5)(3x)² - 1/5 = 4/25

To simplify, let's first square the term (3x):

(2/5)(9x²) - 1/5 = 4/25

Multiplying both sides by the reciprocal of (2/5), which is (5/2):

(5/2)(2/5)(9x²) - (5/2)(1/5) = (5/2)(4/25)

Simplifying:

9x² - 1/5 = 2/5

Adding 1/5 to both sides:

9x² = 2/5 + 1/5

Simplifying:

9x² = 3/5

Dividing both sides by 9:

x² = (3/5)(1/9)

Simplifying:

x² = 1/15

Taking the square root of both sides:

x = ±√(1/15)

Therefore, the solutions to the third equation are x = √(1/15) and x = -√(1/15).