Solve using Quadratic formula, or inferring?

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Given curve: $y = \frac{1}{4} x^2 + 2x + 3$ and associated table of values:

x -8 -6 -4 -2 0 2
y 3 0 -1 0 3 8

Write down one solution of: $\frac{x}{2}+2 = \frac{1}{4} x^2 + 2x + 3$

  • Do we rearrange and use the quadratic formula, $x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}$, to find a solution?
  • Or can we infer/derive a solution from the table of values?