3x 2 −2x−1=3x+1

Sure, let's solve the equation step by step:

1. First, let's rearrange the equation to bring all terms to one side. This gives us:

   3x^2 - 2x - 1 - 3x - 1 = 0

2. Simplify the equation:

   3x^2 - 5x - 2 = 0

3. Now, we need to solve this quadratic equation. We can use the quadratic formula, which is x = [-b ± sqrt(b^2 - 4ac)] / (2a). In our equation, a = 3, b = -5, and c = -2.

4. Calculate the discriminant (b^2 - 4ac):

   (-5)^2 - 43(-2) = 25 + 24 = 49

5. Since the discriminant is positive, we have two real solutions. Let's find them:

   x1 = [5 + sqrt(49)] / (23) = 4 x2 = [5 - sqrt(49)] / (23) = -1/3

So, the solutions to the equation 3x^2 - 2x - 1 = 3x + 1 are x = 4 and x = -1/3.