To solve the quadratic equation 3x² + 15x - 75 = 0, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

Here, a = 3, b = 15, and c = -75. Plugging these values into the formula:

x = (-15 ± √(15² - 4(3)(-75))) / 2(3)
x = (-15 ± √(225 + 900)) / 6
x = (-15 ± √1125) / 6
x = (-15 ± 33.54) / 6

Therefore, the roots of the quadratic equation 3x² + 15x - 75 = 0 are:

x = (-15 + 33.54) / 6 = 3.59
x = (-15 - 33.54) / 6 = -9.59

So, the solutions are x = 3.59 and x = -9.59.