(m-2)x^2-(m+5)x+8=0

Lösung

(m - 2) x^{2} - (m + 5) x + 8 = 0

x = \frac{m + 5 + m ^{2} - 22 m + 89}{2 ( m - 2 )}, x = \frac{m + 5 - m ^{2} - 22 m + 89}{2 ( m - 2 )}; m \neq = 2

Schritte zur Lösung

(m - 2) x^{2} - (m + 5) x + 8 = 0

Löse mit der quadratischen Formel

x_{1, 2} = \frac{- ( - m - 5 ) \pm ( - m - 5 ) ^{2} - 4 ( m - 2 ) \cdot 8}{2 ( m - 2 )}

Vereinfache

(- m - 5)^{2} - 4 (m - 2) \cdot 8 : m^{2} - 22 m + 89

x_{1, 2} = \frac{- ( - m - 5 ) \pm m ^{2} - 22 m + 89}{2 ( m - 2 )}; m \neq = 2

Trenne die Lösungen

x_{1} = \frac{- ( - m - 5 ) + m ^{2} - 22 m + 89}{2 ( m - 2 )}, x_{2} = \frac{- ( - m - 5 ) - m ^{2} - 22 m + 89}{2 ( m - 2 )}

x = \frac{- ( - m - 5 ) + m ^{2} - 22 m + 89}{2 ( m - 2 )} : \frac{m + 5 + m ^{2} - 22 m + 89}{2 ( m - 2 )}

x = \frac{- ( - m - 5 ) - m ^{2} - 22 m + 89}{2 ( m - 2 )} : \frac{m + 5 - m ^{2} - 22 m + 89}{2 ( m - 2 )}

Die Lösungen für die quadratische Gleichung sind:

x = \frac{m + 5 + m ^{2} - 22 m + 89}{2 ( m - 2 )}, x = \frac{m + 5 - m ^{2} - 22 m + 89}{2 ( m - 2 )}; m \neq = 2

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