1. You can complete the square.
x² - 2x = 24
x² - 2x + 1 = 25 . . . . . add 1 to complete the square
(x -1)² = 25
x = 1 ± √25 = 1 ±5
x = -4, 6
2. You can use the quadratic formula.
2x² -9x +8 = 0 . . . . . . a = 2, b = -9, c = 8
The quadratic formula tells you
x = (-b ±√(b² -4ac))/(2a)
x = (-(-9) ±√((-9)² -4(2)(8)))/(2(2))
x = (9 ±√17)/4
