Final answer:
The quadratic equation 3x²-4x-1=0 can be solved using the quadratic formula, with a=3, b=-4, and c=-1. The two solutions are x = (4 + 2√7) / 6 and x = (4 - 2√7) / 6.
Step-by-step explanation:
To solve the quadratic equation 3x²-4x-1=0 using the quadratic formula, we first identify the coefficients: a=3, b=-4, and c=-1. The quadratic formula is given by x = (-b ± √(b² - 4ac)) / (2a). Substituting our values into the formula, we get:
x = (4 ± √((-4)² - 4(3)(-1))) / (2(3))
x = (4 ± √(16 + 12)) / 6
x = (4 ± √(28)) / 6
x = (4 ± 2√7) / 6
Therefore, the two solutions for the equation are:
- x = (4 + 2√7) / 6
- x = (4 - 2√7) / 6