Solve: $\;$ $6 \sin^{-1} \left(x^2 - 6x + 8.5\right) = \pi$
Given equation: $\;$ $6 \sin^{-1} \left(x^2 - 6x + 8.5\right) = \pi$
i.e. $\;$ $\sin^{-1} \left(x^2 - 6x + 8.5\right) = \dfrac{\pi}{6}$
i.e. $\;$ $x^2 - 6x + 8.5 = \sin \left(\dfrac{\pi}{6}\right)$
i.e. $\;$ $x^2 - 6x + 8.5 = 0.5$
i.e. $\;$ $x^2 - 6x + 8 = 0$
i.e. $\;$ $\left(x - 4\right) \left(x - 2\right) = 0$
i.e. $\;$ $x = 4$ $\;$ or $\;$ $x = 2$