Quadratische Gleichungen: 6·z^2 + 23·z = 18 und 0.5·x^2 - x = 12

Question

Ich brauche bei diesen Aufgaben bitte Hilfe:

a)    6 z² + 23 z = 18

b)    0,5 x² - x = 12

Answer 1

6·z^2 + 23·z = 18

6·z^2 + 23·z - 18 = 0

z^2 + 23/6·z - 3 = 0

z = -23/12 ± √((23/12)^2 + 3) = - 23/12 ± 31/12

z = 2/3 ∨ z = -9/2

Comments

0.5·x^2 - x = 12

0.5·x^2 - x - 12 = 0

x^2 - 2x - 24 = 0

x = 1 ± √(1 + 24) = 1 ± 5

x = 6 ∨ x = -4

Answer 2

b)    0,5 x² - x = 12 I·2

x²-2x-24=0 pq-Formel

x_1/2=1±√(1+24)

x₁= 6; x₂=-4

Answer 3

6 z² + 23 z = 18 | -18

6 z² + 23 z - 18 =0 |:6

 z² + 23/6  z - 3 =0 ->pq-Formel

z1,2= (-23)/12 ± √ (961/144)

z1,2= (-23)/12 ± 31/12

z1= 2/3

z2= -9/2