x 2 −2x−52=3x−2

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

1. First, let's rewrite the equation: x^2 - 2x - 52 = 3x - 2
2. Next, let's move all terms to one side of the equation: x^2 - 2x - 3x + 52 + 2 = 0
3. Simplify the equation: x^2 - 5x + 54 = 0
4. Now, we can solve the equation by factoring: (x - 6)(x + 9) = 0
5. Set each factor equal to zero and solve for x: x - 6 = 0, so x = 6 and x + 9 = 0, so x = -9

So, the solutions to the equation are x = 6 and x = -9.