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Math·Advanced Math·Nonlinear equations in one variable and systems of equations in two variables

hard

$$\frac{1}{3}{x}^2-7x+k=5$$
In the given equation, $k$ is a constant. A solution to the equation is $\frac{21}{2}-\frac{3\sqrt{73}}{2}$. What is the value of $k$?

A

$13$

B

$5$

C

$-13$

D

$-18$