Solve for x: $(x - 3) (x - 4)^{2} (x - 5) - 6 = 0$

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Solution

$(x - 3) {(x - 4)}^{2} (x - 5) - 6 = 0$

$x^{4} - 16 x^{3} + 95 x^{2} - 248 x + 234 = 0$

$x^{3} - 13.73205 \dots x^{2} + 63.85641 \dots x - 103.17691 \dots \approx 0$

$x^{2} - 8 x + 18 \approx 0$

$x = - \sqrt{3} + 4, x = \sqrt{3} + 4$

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