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

Lösung

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

x = \frac{- m + 7 + m ^{2} - 22 m + 73}{2 ( m - 3 )}, x = \frac{- m + 7 - m ^{2} - 22 m + 73}{2 ( m - 3 )}; m \neq = 3

Schritte zur Lösung

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

Löse mit der quadratischen Formel

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

Vereinfache

(m - 7)^{2} - 4 (m - 3) \cdot 2 : m^{2} - 22 m + 73

x_{1, 2} = \frac{- ( m - 7 ) \pm m ^{2} - 22 m + 73}{2 ( m - 3 )}; m \neq = 3

Trenne die Lösungen

x_{1} = \frac{- ( m - 7 ) + m ^{2} - 22 m + 73}{2 ( m - 3 )}, x_{2} = \frac{- ( m - 7 ) - m ^{2} - 22 m + 73}{2 ( m - 3 )}

x = \frac{- ( m - 7 ) + m ^{2} - 22 m + 73}{2 ( m - 3 )} : \frac{- m + 7 + m ^{2} - 22 m + 73}{2 ( m - 3 )}

x = \frac{- ( m - 7 ) - m ^{2} - 22 m + 73}{2 ( m - 3 )} : \frac{- m + 7 - m ^{2} - 22 m + 73}{2 ( m - 3 )}

Die Lösungen für die quadratische Gleichung sind:

x = \frac{- m + 7 + m ^{2} - 22 m + 73}{2 ( m - 3 )}, x = \frac{- m + 7 - m ^{2} - 22 m + 73}{2 ( m - 3 )}; m \neq = 3

2 x^{2} - 3 x = - 5

5 x^{2} + 7 = 27

0 = - x^{2} + 5 x - 4

2 n^{2} + 15 n + 7 = 0

x^{2} + m x + 7 = 0, m > 0