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Online ProgramJames was solving the following problem and came up with *no solution* as an answer. His answer is incorrect. Find his mistake, tell how to correct it, and give the right answer to the problem.

In a certain area of the city, traffic increases or decreases depending on the time of day based on the formula \(x^2-12x-6=y\). Meanwhile the number of traffic tickets given at time (x) is given as y = 2x + 1. The value of y when both graphs intersect represents the number of tickets given out. What is the largest of these values?

**James' work:**

x^{2} - 12x - 6 = 2x + 1

x^{2 }-14x - 7 = 0

Plug into the quadratic formula using a = 1, b = -14, c = -7

\(x=\frac{-(-14)\pm \sqrt{{-14}^2-4(1)(-7)}}{2(1)}\)

\(x=\frac{14\pm \sqrt{-168}}{2}\)

This problem has no real solution because the discriminant

\(-{14}^2-4\left(1\right)\left(-7\right)=-168\). When you get a negative number for the discriminant there is no real answer to the problem.