a)
x2 - 2x - 8 = 0
D = (-2)2 - 4 * 1 * (-8) = 4 + 32 = 36 = 62
x1,2 = (2 ± 6) / 2
x1 = (2 + 6) / 2 = 8 / 2 = 4
x2 = (2 - 6) / 2 = -4 / 2 = -2

b)
x2 + 5x - 14 = 0
D = 52 - 4 * 1 * (-14) = 25 + 56 = 81 = 92
x1,2 = (-5 ± 9) / 2
x1 = (-5 + 9) / 2 = 4 / 2 = 2
x2 = (-5 - 9) / 2 = -14 / 2 = -7

c)
x2 - 4x + 4 = 0
D = (-4)2 - 4 * 1 * 4 = 16 - 16 = 0 = 02
x1,2 = (4 ± 0) / 2
x1 = (4 + 0) / 2 = 4 / 2 = 2
x2 = (4 - 0) / 2 = 4 / 2 = 2

d)
x2 - 4x + 3 = 0
D = (-4)2 - 4 * 1 * 3 = 16 - 12 = 4 = 22
x1,2 = (4 ± 2) / 2
x1 = (4 + 2) / 2 = 6 / 2 = 3
x2 = (4 - 2) / 2 = 2 / 2 = 1

e)
2x2 - 3x - 2 = 0
D = (-3)2 - 4 * 2 * (-2) = 9 + 16 = 25 = 52
x1,2 = (3 ± 5) / (2 * 2)
x1 = (3 + 5) / 4 = 8 / 4 = 2
x2 = (3 - 5) / 4 = -2 / 4 = -1/2 = -0,5

f)
5x2 + 10x + 5 = 0 /:5
x2 + 2x + 1 = 0
D = 22 - 4 * 1 * 1 = 4 - 4 = 0 = 02
x1,2 = (-2 ± 0) / 2
x1 = (-2 + 0) / 2 = -2 / 2 = -1
x2 = (-2 - 0) / 2 = -2 / 2 = -1

g)
x2 - x + 4 = 2x - 2 0-ra rendezzük / - 2x /+ 2
x2 - 3x + 6 = 0
D = (-3)2 - 4 * 1 * 6 = 9 - 24 = -15 Nincs megoldás, mert a diszkrimináns negatív.

h)
x2 - 2x + 10 = 5x - 2 0-ra rendezzük / - 5x / + 2
x2 - 7x + 12 = 0
D = (-7)2 - 4 * 1 * 12 = 49 - 48 = 1 = 12
x1,2 = (7 ± 1) / 2
x1 = (7 + 1) / 2 = 8 / 2 = 4
x2 = (7 - 1) / 2 = 6 / 2 = 3

i)
x2 - 9 = 0
D = 02 - 4 * 1 * (-9) = 0 + 36 = 36 = 62
x1,2 = (0 ± 6) / 2
x1 = (0 + 6) / 2 = 6 / 2 = 3
x2 = (0 - 6) / 2 = -6 / 2 = -3

Másik megoldás:
x2 - 9 = 0 Szorzattá alakítjuk azonosság alkalmazásával, mert hiányos másodfokú egyenlet:
x2 - 32 = 0
(x - 3) * (x + 3) = 0
Szorzat akkor egyenlő 0-val, ha valamelyik szorzótényező 0, azaz:
x - 3 = 0
x1 = 3
vagy
x + 3 = 0
x2 = -3

j)
x2 - 4x = 0
D = (-4)2 - 4 * 1 * 0 = 16 - 0 = 16 = 42
x1,2 = (4 ± 4) / 2
x1 = (4 + 4) / 2 = 8 / 2 = 4
x2 = (4 - 4) / 2 = 0 / 2 = 0

Másik megoldás:
x2 - 4x = 0 Szorzattá alakítjuk kiemelésserl, mert hiányos másodfokú egyenlet:
x * (x - 4) = 0
Szorzat akkor egyenlő 0-val, ha valamelyik szorzótényező 0, azaz:
x1 = 0
vagy
x - 4 = 0
x2 = 4