Answer:
To solve the quadratic equation 12x^2 - 5x - 2 = 0, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac))/(2a)
In this case, a = 12, b = -5, and c = -2.
Substituting the values into the formula:
x = (-(-5) ± √((-5)^2 - 4(12)(-2)))/(2(12))
x = (5 ± √(25 + 96))/(24)
x = (5 ± √121)/(24)
Now we can simplify the square root:
x = (5 ± 11)/(24)
This gives two solutions:
x₁ = (5 + 11)/24 = 16/24 = 2/3
x₂ = (5 - 11)/24 = -6/24 = -1/4
Therefore, the solutions to the quadratic equation 12x^2 - 5x - 2 = 0 are x = 2/3 and x = -1/4.