(a+5)x^2+(a+3)x+7-3a=0

Lösung

(a + 5) x^{2} + (a + 3) x + 7 - 3 a = 0

x = \frac{- a - 3 + 13 a ^{2} + 38 a - 131}{2 ( a + 5 )}, x = \frac{- a - 3 - 13 a ^{2} + 38 a - 131}{2 ( a + 5 )}; a \neq = - 5

Schritte zur Lösung

(a + 5) x^{2} + (a + 3) x + 7 - 3 a = 0

Löse mit der quadratischen Formel

x_{1, 2} = \frac{- ( a + 3 ) \pm ( a + 3 ) ^{2} - 4 ( a + 5 ) ( 7 - 3 a )}{2 ( a + 5 )}

Vereinfache

(a + 3)^{2} - 4 (a + 5) (7 - 3 a) : 13 a^{2} + 38 a - 131

x_{1, 2} = \frac{- ( a + 3 ) \pm 13 a ^{2} + 38 a - 131}{2 ( a + 5 )}; a \neq = - 5

Trenne die Lösungen

x_{1} = \frac{- ( a + 3 ) + 13 a ^{2} + 38 a - 131}{2 ( a + 5 )}, x_{2} = \frac{- ( a + 3 ) - 13 a ^{2} + 38 a - 131}{2 ( a + 5 )}

x = \frac{- ( a + 3 ) + 13 a ^{2} + 38 a - 131}{2 ( a + 5 )} : \frac{- a - 3 + 13 a ^{2} + 38 a - 131}{2 ( a + 5 )}

x = \frac{- ( a + 3 ) - 13 a ^{2} + 38 a - 131}{2 ( a + 5 )} : \frac{- a - 3 - 13 a ^{2} + 38 a - 131}{2 ( a + 5 )}

Die Lösungen für die quadratische Gleichung sind:

x = \frac{- a - 3 + 13 a ^{2} + 38 a - 131}{2 ( a + 5 )}, x = \frac{- a - 3 - 13 a ^{2} + 38 a - 131}{2 ( a + 5 )}; a \neq = - 5

x^{2} - 120 x + 3600 = 0

x^{2} - 3 x = 2 x + 14

23 = x^{2} + 7

so l v e f or x, 432 = 3 x^{2}

X^{2} + 3 X + 2 = 0