(2m-11)x^2-3(m+4)x+(m-3)=0

Lösung

(2 m - 11) x^{2} - 3 (m + 4) x + (m - 3) = 0

x = \frac{3 m + 12 + m ^{2} + 140 m + 12}{2 ( 2 m - 11 )}, x = \frac{3 m + 12 - m ^{2} + 140 m + 12}{2 ( 2 m - 11 )}; m \neq = \frac{11}{2}

Schritte zur Lösung

(2 m - 11) x^{2} - 3 (m + 4) x + (m - 3) = 0

Schreibe

(2 m - 11) x^{2} - 3 (m + 4) x + (m - 3)

um:

2 m x^{2} - 11 x^{2} - 3 m x - 12 x + m - 3

2 m x^{2} - 11 x^{2} - 3 m x - 12 x + m - 3 = 0

Schreibe in der Standard Form

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

(2 m - 11) x^{2} - (3 m + 12) x + m - 3 = 0

Löse mit der quadratischen Formel

x_{1, 2} = \frac{- ( - 3 m - 12 ) \pm ( - 3 m - 12 ) ^{2} - 4 ( 2 m - 11 ) ( m - 3 )}{2 ( 2 m - 11 )}

Vereinfache

(- 3 m - 12)^{2} - 4 (2 m - 11) (m - 3) : m^{2} + 140 m + 12

x_{1, 2} = \frac{- ( - 3 m - 12 ) \pm m ^{2} + 140 m + 12}{2 ( 2 m - 11 )}; m \neq = \frac{11}{2}

Trenne die Lösungen

x_{1} = \frac{- ( - 3 m - 12 ) + m ^{2} + 140 m + 12}{2 ( 2 m - 11 )}, x_{2} = \frac{- ( - 3 m - 12 ) - m ^{2} + 140 m + 12}{2 ( 2 m - 11 )}

x = \frac{- ( - 3 m - 12 ) + m ^{2} + 140 m + 12}{2 ( 2 m - 11 )} : \frac{3 m + 12 + m ^{2} + 140 m + 12}{2 ( 2 m - 11 )}

x = \frac{- ( - 3 m - 12 ) - m ^{2} + 140 m + 12}{2 ( 2 m - 11 )} : \frac{3 m + 12 - m ^{2} + 140 m + 12}{2 ( 2 m - 11 )}

Die Lösungen für die quadratische Gleichung sind:

x = \frac{3 m + 12 + m ^{2} + 140 m + 12}{2 ( 2 m - 11 )}, x = \frac{3 m + 12 - m ^{2} + 140 m + 12}{2 ( 2 m - 11 )}; m \neq = \frac{11}{2}

3 x^{2} = - 6 - 8 x

11 x^{2} + 5 = 49

so l v e f or a, (a + b)^{2} = 49 + 12 b

h^{2} + 5 h = 155

h^{2} - 7 h = 0