x^2+2/3 ax+(-(a^2)/2+1)=0

Lösung

x^{2} + \frac{2}{3} a x + (- \frac{a ^{2}}{2} + 1) = 0

x = \frac{- a + a ^{2} - 3 ( - \frac{3 a ^{2}}{2} + 3 )}{3}, x = - \frac{a + a ^{2} - 3 ( - \frac{3 a ^{2}}{2} + 3 )}{3}

Schritte zur Lösung

x^{2} + \frac{2}{3} a x + (- \frac{a ^{2}}{2} + 1) = 0

Multipliziere beide Seiten mit

3

3 x^{2} + 2 a x + 3 (- \frac{a ^{2}}{2} + 1) = 0

Schreibe

3 x^{2} + 2 a x + 3 (- \frac{a ^{2}}{2} + 1)

um:

3 x^{2} + 2 a x - \frac{3 a ^{2}}{2} + 3

3 x^{2} + 2 a x - \frac{3 a ^{2}}{2} + 3 = 0

Löse mit der quadratischen Formel

x_{1, 2} = \frac{- 2 a \pm ( 2 a ) ^{2} - 4 \cdot 3 ( - \frac{3 a ^{2}}{2} + 3 )}{2 \cdot 3}

Vereinfache

(2 a)^{2} - 4 \cdot 3 (- \frac{3 a ^{2}}{2} + 3) : 2 a^{2} - 3 (3 - \frac{3 a ^{2}}{2})

x_{1, 2} = \frac{- 2 a \pm 2 a ^{2} - 3 ( 3 - \frac{3 a ^{2}}{2} )}{2 \cdot 3}

Trenne die Lösungen

x_{1} = \frac{- 2 a + 2 a ^{2} - 3 ( 3 - \frac{3 a ^{2}}{2} )}{2 \cdot 3}, x_{2} = \frac{- 2 a - 2 a ^{2} - 3 ( 3 - \frac{3 a ^{2}}{2} )}{2 \cdot 3}

x = \frac{- 2 a + 2 a ^{2} - 3 ( 3 - \frac{3 a ^{2}}{2} )}{2 \cdot 3} : \frac{- a + a ^{2} - 3 ( - \frac{3 a ^{2}}{2} + 3 )}{3}

x = \frac{- 2 a - 2 a ^{2} - 3 ( 3 - \frac{3 a ^{2}}{2} )}{2 \cdot 3} : - \frac{a + a ^{2} - 3 ( - \frac{3 a ^{2}}{2} + 3 )}{3}

Die Lösungen für die quadratische Gleichung sind:

x = \frac{- a + a ^{2} - 3 ( - \frac{3 a ^{2}}{2} + 3 )}{3}, x = - \frac{a + a ^{2} - 3 ( - \frac{3 a ^{2}}{2} + 3 )}{3}

x (x - 5) - 4 (3 - x) = 0

1 = \frac{x ^{2}}{4}

co m pl e t es q u a re x^{2} + 20 x + 28 = 9

6 x^{2} + 17 x + 7 = 0

2 0^{2} + 2 0^{2} = x^{2}