Final answer:
To solve the equation 9x^2 - 3x - 2 = 0, use the quadratic formula to find the values of x.
Step-by-step explanation:
To solve the equation 9x^2 - 3x - 2 = 0, we can use the quadratic formula.
The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For the given equation, a = 9, b = -3, and c = -2. Substituting these values into the quadratic formula, we get:
x = (-(-3) ± √((-3)^2 - 4(9)(-2))) / (2(9))
Simplifying the equation gives us:
x = (3 ± √(9 + 72)) / 18
Finally, the two solutions for x are:
x ≈ 0.56 and x ≈ -0.78