To solve these quadratic equations, we can use the quadratic formula:

For the equation 10x^2 - 9x + 2 = 0:

a = 10, b = -9, c = 2

The quadratic formula is:

x = (-b ± √(b^2 - 4ac)) / 2a

Plugging in the values:

x = (9 ± √((-9)^2 - 4102)) / (2*10)
x = (9 ± √(81 - 80)) / 20
x = (9 ± √1) / 20
x = (9 ± 1) / 20

Therefore, the solutions are:
x1 = (9 + 1) / 20 = 10 / 20 = 0.5
x2 = (9 - 1) / 20 = 8 / 20 = 0.4

For the equation 21x^2 - 2x - 3 = 0:

a = 21, b = -2, c = -3

Using the quadratic formula again:

x = (2 ± √((-2)^2 - 421-3)) / (2*21)
x = (2 ± √(4 + 252)) / 42
x = (2 ± √256) / 42
x = (2 ± 16) / 42

Therefore, the solutions are:
x1 = (2 + 16) / 42 = 18 / 42 = 3 / 7
x2 = (2 - 16) / 42 = -14 / 42 = -1 / 3

Thus, the solutions for the equations are:
10x^2 - 9x + 2 = 0 → x1 = 0.5, x2 = 0.4
21x^2 - 2x - 3 = 0 → x1 = 3/7, x2 = -1/3