Solving a quadratic using a system of equations

Algebra Level 3

If {a+b=40b+c=3a+c=11 \begin{cases} a + b = 40 \\ b + c = 3 \\ a + c = -11 \end{cases} where aa, bb and cc are real numbers, and that a+b+c=k a + b + c = k , then find xx that satisfies the following equation.

kx2444kx+1933k=48 \frac{kx^2}{4} - 44kx + 1933k = -48

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