-3x^2+(7k^2-3)x+7=0

Lösung

- 3 x^{2} + (7 k^{2} - 3) x + 7 = 0

x = - \frac{- 7 k ^{2} + 3 + 49 k ^{4} - 42 k ^{2} + 93}{6}, x = - \frac{- 7 k ^{2} + 3 - 49 k ^{4} - 42 k ^{2} + 93}{6}

Schritte zur Lösung

- 3 x^{2} + (7 k^{2} - 3) x + 7 = 0

Löse mit der quadratischen Formel

x_{1, 2} = \frac{- ( 7 k ^{2} - 3 ) \pm ( 7 k ^{2} - 3 ) ^{2} - 4 ( - 3 ) \cdot 7}{2 ( - 3 )}

Vereinfache

(7 k^{2} - 3)^{2} - 4 (- 3) \cdot 7 : 49 k^{4} - 42 k^{2} + 93

x_{1, 2} = \frac{- ( 7 k ^{2} - 3 ) \pm 49 k ^{4} - 42 k ^{2} + 93}{2 ( - 3 )}

Trenne die Lösungen

x_{1} = \frac{- ( 7 k ^{2} - 3 ) + 49 k ^{4} - 42 k ^{2} + 93}{2 ( - 3 )}, x_{2} = \frac{- ( 7 k ^{2} - 3 ) - 49 k ^{4} - 42 k ^{2} + 93}{2 ( - 3 )}

x = \frac{- ( 7 k ^{2} - 3 ) + 49 k ^{4} - 42 k ^{2} + 93}{2 ( - 3 )} : - \frac{- 7 k ^{2} + 3 + 49 k ^{4} - 42 k ^{2} + 93}{6}

x = \frac{- ( 7 k ^{2} - 3 ) - 49 k ^{4} - 42 k ^{2} + 93}{2 ( - 3 )} : - \frac{- 7 k ^{2} + 3 - 49 k ^{4} - 42 k ^{2} + 93}{6}

Die Lösungen für die quadratische Gleichung sind:

x = - \frac{- 7 k ^{2} + 3 + 49 k ^{4} - 42 k ^{2} + 93}{6}, x = - \frac{- 7 k ^{2} + 3 - 49 k ^{4} - 42 k ^{2} + 93}{6}

(x + 1)^{3} = (x + 2)^{3} - 1

x^{2} + 3 x = 20 x

6 - \frac{x ^{2}}{4} = 2

co m pl e t es q u a re p^{2} + 16 p - 22 = 0

3 x (x - 2) = 9 x^{2} - 7 x