Solve the Quadratic Equation: Find x in 3x^2 - 17x + 28 = x + 4

To solve the equation $3x^2 - 17x + 28 = x + 4$, follow these steps:

• Step 1: Simplify the equation.
  Begin by moving all terms to one side of the equation to obtain a standard form quadratic equation:
  $3x^2 - 17x + 28 - x - 4 = 0$
• Simplify further:
  $3x^2 - 18x + 24 = 0$
• Step 2: Identify coefficients.
  The equation is now in the standard form $ax^2 + bx + c = 0$ where $a = 3$, $b = -18$, and $c = 24$.
• Step 3: Use the quadratic formula to solve for $x$.
  The quadratic formula is given by:
  $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
• Calculate the discriminant $b^2 - 4ac$:
  $(-18)^2 - 4(3)(24) = 324 - 288 = 36$
• Since the discriminant is positive, there are two solutions.
• Apply the quadratic formula:
  $x = \frac{-(-18) \pm \sqrt{36}}{2(3)} = \frac{18 \pm 6}{6}$
• Calculate the two possible solutions:
  $x_1 = \frac{18 + 6}{6} = 4$
  $x_2 = \frac{18 - 6}{6} = 2$

Therefore, the solutions to the equation are $x_1 = 4$ and $x_2 = 2$.