(a+1)x^2+(a-2)x+2a+3=0

Lösung

(a + 1) x^{2} + (a - 2) x + 2 a + 3 = 0

x = \frac{- a + 2 + - 7 a ^{2} - 24 a - 8}{2 ( a + 1 )}, x = \frac{- a + 2 - - 7 a ^{2} - 24 a - 8}{2 ( a + 1 )}; a \neq = - 1

Schritte zur Lösung

(a + 1) x^{2} + (a - 2) x + 2 a + 3 = 0

Löse mit der quadratischen Formel

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

Vereinfache

(a - 2)^{2} - 4 (a + 1) (2 a + 3) : - 7 a^{2} - 24 a - 8

x_{1, 2} = \frac{- ( a - 2 ) \pm - 7 a ^{2} - 24 a - 8}{2 ( a + 1 )}; a \neq = - 1

Trenne die Lösungen

x_{1} = \frac{- ( a - 2 ) + - 7 a ^{2} - 24 a - 8}{2 ( a + 1 )}, x_{2} = \frac{- ( a - 2 ) - - 7 a ^{2} - 24 a - 8}{2 ( a + 1 )}

x = \frac{- ( a - 2 ) + - 7 a ^{2} - 24 a - 8}{2 ( a + 1 )} : \frac{- a + 2 + - 7 a ^{2} - 24 a - 8}{2 ( a + 1 )}

x = \frac{- ( a - 2 ) - - 7 a ^{2} - 24 a - 8}{2 ( a + 1 )} : \frac{- a + 2 - - 7 a ^{2} - 24 a - 8}{2 ( a + 1 )}

Die Lösungen für die quadratische Gleichung sind:

x = \frac{- a + 2 + - 7 a ^{2} - 24 a - 8}{2 ( a + 1 )}, x = \frac{- a + 2 - - 7 a ^{2} - 24 a - 8}{2 ( a + 1 )}; a \neq = - 1

x^{2} = 48 - 2 x

2 x^{2} - 35 = 1

4 x^{2} + 21 = 5 x

f^{2} = 16

2 5^{2} + 6 0^{2} = x^{2}