(m+3)x^2-(2m-5)x+2m-10=0

Lösung

(m + 3) x^{2} - (2 m - 5) x + 2 m - 10 = 0

x = \frac{2 m - 5 + - 4 m ^{2} - 4 m + 145}{2 ( m + 3 )}, x = \frac{2 m - 5 - - 4 m ^{2} - 4 m + 145}{2 ( m + 3 )}; m \neq = - 3

Schritte zur Lösung

(m + 3) x^{2} - (2 m - 5) x + 2 m - 10 = 0

Schreibe

(m + 3) x^{2} - (2 m - 5) x + 2 m - 10

um:

m x^{2} + 3 x^{2} - 2 m x + 5 x + 2 m - 10

m x^{2} + 3 x^{2} - 2 m x + 5 x + 2 m - 10 = 0

Schreibe in der Standard Form

a x^{2} + b x + c = 0

(m + 3) x^{2} + (- 2 m + 5) x + 2 m - 10 = 0

Löse mit der quadratischen Formel

x_{1, 2} = \frac{- ( - 2 m + 5 ) \pm ( - 2 m + 5 ) ^{2} - 4 ( m + 3 ) ( 2 m - 10 )}{2 ( m + 3 )}

Vereinfache

(- 2 m + 5)^{2} - 4 (m + 3) (2 m - 10) : - 4 m^{2} - 4 m + 145

x_{1, 2} = \frac{- ( - 2 m + 5 ) \pm - 4 m ^{2} - 4 m + 145}{2 ( m + 3 )}; m \neq = - 3

Trenne die Lösungen

x_{1} = \frac{- ( - 2 m + 5 ) + - 4 m ^{2} - 4 m + 145}{2 ( m + 3 )}, x_{2} = \frac{- ( - 2 m + 5 ) - - 4 m ^{2} - 4 m + 145}{2 ( m + 3 )}

x = \frac{- ( - 2 m + 5 ) + - 4 m ^{2} - 4 m + 145}{2 ( m + 3 )} : \frac{2 m - 5 + - 4 m ^{2} - 4 m + 145}{2 ( m + 3 )}

x = \frac{- ( - 2 m + 5 ) - - 4 m ^{2} - 4 m + 145}{2 ( m + 3 )} : \frac{2 m - 5 - - 4 m ^{2} - 4 m + 145}{2 ( m + 3 )}

Die Lösungen für die quadratische Gleichung sind:

x = \frac{2 m - 5 + - 4 m ^{2} - 4 m + 145}{2 ( m + 3 )}, x = \frac{2 m - 5 - - 4 m ^{2} - 4 m + 145}{2 ( m + 3 )}; m \neq = - 3

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