Polynomial

x⁴ - 5x³ + 5x² + 17x - 42 - x⁴ + 5x³ - 4x² - 16x + 20

= x⁴ - x⁴ - 5x³ + 5x³ + 5x² - 4x² + 17x - 16x - 42 + 20

= x² + x - 22

$x = \frac{-1 + \sqrt{89}}{2}$

$x = \frac{-1 - \sqrt{89}}{2}$