x 2 −12x+51=2x+3

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

1. First, let's simplify the equation by bringing all terms to one side. We subtract 2x and 3 from both sides:

   x^2 - 12x + 51 - 2x - 3 = 0

2. Combine like terms:

   x^2 - 14x + 48 = 0

3. Now, we need to factor the quadratic equation. We are looking for two numbers that multiply to 48 and add to -14. Those numbers are -6 and -8. So, we can write the equation as:

   (x - 6)(x - 8) = 0

4. Finally, we set each factor equal to zero and solve for x:

   x - 6 = 0 => x = 6

   x - 8 = 0 => x = 8

So, the solutions to the equation are x = 6 and x = 8.