Let's solve each quadratic equation for x.

1) 2x² + 3x - 5 = 0
The solutions are:
x = (-(3) ± √(3² - 4(2)(-5))) / (2(2))
x = (-3 ± √(9 + 40)) / 4
x = (-3 ± √49) / 4
x = (-3 ± 7) / 4
x = 4 or x = -1.5

2) 3x² + 2x - 5 = 0
The solutions are:
x = (-(2) ± √(2² - 4(3)(-5))) / (2(3))
x = (-2 ± √(4 + 60)) / 6
x = (-2 ± √64) / 6
x = (-2 ± 8) / 6
x = 1 or x = -5/3

3) 6x² + x - 1 = 0
The solutions are:
x = (-(1) ± √(1² - 4(6)(-1))) / (2(6))
x = (-1 ± √(1 + 24)) / 12
x = (-1 ± √25) / 12
x = (-1 ± 5) / 12
x = 2/3 or x = -1/2

4) x² - 5x -1 = 0
The solutions are:
x = (5 ± √(5² - 4(1)(-1))) / (2(1))
x = (5 ± √(25 + 4)) / 2
x = (5 ± √29) / 2

5) 3x² + 7x - 6 = 0
The solutions are:
x = (-(7) ± √(7² - 4(3)(-6))) / (2(3))
x = (-7 ± √(49 + 72)) / 6
x = (-7 ± √121) / 6
x = (-7 ± 11) / 6
x = 1 or x = -2

Therefore, the solutions of the given quadratic equations are:
1) x = 4 or x = -1.5
2) x = 1 or x = -5/3
3) x = 2/3 or x = -1/2
4) x = (5 + √29) / 2 or x = (5 - √29) / 2
5) x = 1 or x = -2