To solve the equation 3x^2 + 8x - 3 = 0, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

In this case, the coefficients are:
a = 3
b = 8
c = -3

Plugging these values into the formula, we get:

x = (-8 ± √(8^2 - 43(-3))) / 2*3
x = (-8 ± √(64 + 36)) / 6
x = (-8 ± √100) / 6
x = (-8 ± 10) / 6

There are two possible solutions:

x1 = (-8 + 10) / 6 = 2 / 6 = 1/3
x2 = (-8 - 10) / 6 = -18 / 6 = -3

Therefore, the solutions to the equation 3x^2 + 8x - 3 = 0 are x = 1/3 and x = -3.