$$\sqrt{7}K-17-K=-1$$
$K = \frac{8 {(\sqrt{7} + 1)}}{3} \approx 9.722003496$
$$\sqrt{7}K-K=-1+17$$
$$\sqrt{7}K-K=16$$
$$\left(\sqrt{7}-1\right)K=16$$
$$\frac{\left(\sqrt{7}-1\right)K}{\sqrt{7}-1}=\frac{16}{\sqrt{7}-1}$$
$$K=\frac{16}{\sqrt{7}-1}$$
$$K=\frac{8\sqrt{7}+8}{3}$$
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