(2a+3)x^2-3(a+1)x+4=0

Lösung

(2 a + 3) x^{2} - 3 (a + 1) x + 4 = 0

x = \frac{3 a + 3 + 9 a ^{2} - 14 a - 39}{2 ( 2 a + 3 )}, x = \frac{3 a + 3 - 9 a ^{2} - 14 a - 39}{2 ( 2 a + 3 )}; a \neq = - \frac{3}{2}

Schritte zur Lösung

(2 a + 3) x^{2} - 3 (a + 1) x + 4 = 0

Schreibe

(2 a + 3) x^{2} - 3 (a + 1) x + 4

um:

2 a x^{2} + 3 x^{2} - 3 a x - 3 x + 4

2 a x^{2} + 3 x^{2} - 3 a x - 3 x + 4 = 0

Schreibe in der Standard Form

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

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

Löse mit der quadratischen Formel

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

Vereinfache

(- 3 a - 3)^{2} - 4 (2 a + 3) \cdot 4 : 9 a^{2} - 14 a - 39

x_{1, 2} = \frac{- ( - 3 a - 3 ) \pm 9 a ^{2} - 14 a - 39}{2 ( 2 a + 3 )}; a \neq = - \frac{3}{2}

Trenne die Lösungen

x_{1} = \frac{- ( - 3 a - 3 ) + 9 a ^{2} - 14 a - 39}{2 ( 2 a + 3 )}, x_{2} = \frac{- ( - 3 a - 3 ) - 9 a ^{2} - 14 a - 39}{2 ( 2 a + 3 )}

x = \frac{- ( - 3 a - 3 ) + 9 a ^{2} - 14 a - 39}{2 ( 2 a + 3 )} : \frac{3 a + 3 + 9 a ^{2} - 14 a - 39}{2 ( 2 a + 3 )}

x = \frac{- ( - 3 a - 3 ) - 9 a ^{2} - 14 a - 39}{2 ( 2 a + 3 )} : \frac{3 a + 3 - 9 a ^{2} - 14 a - 39}{2 ( 2 a + 3 )}

Die Lösungen für die quadratische Gleichung sind:

x = \frac{3 a + 3 + 9 a ^{2} - 14 a - 39}{2 ( 2 a + 3 )}, x = \frac{3 a + 3 - 9 a ^{2} - 14 a - 39}{2 ( 2 a + 3 )}; a \neq = - \frac{3}{2}

3 x^{2} - 2 x + 1 = 2 x^{2} - 3 x + 7

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

x^{1} + x^{2} = 5

so l v e f or x, x^{2} - 4 y^{2} - z = 0

so l v e f or x, y^{n} = 2 x^{2}