12ax^2+8ax+12bx+4b+12c=0

Lösung

12 a x^{2} + 8 a x + 12 b x + 4 b + 12 c = 0

x = \frac{- 2 a - 3 b + 4 a ^{2} - 36 a c + 9 b ^{2}}{6 a}, x = - \frac{2 a + 3 b + 4 a ^{2} - 36 a c + 9 b ^{2}}{6 a}; a \neq = 0

Schritte zur Lösung

12 a x^{2} + 8 a x + 12 b x + 4 b + 12 c = 0

Schreibe in der Standard Form

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

12 a x^{2} + (8 a + 12 b) x + 4 b + 12 c = 0

Löse mit der quadratischen Formel

x_{1, 2} = \frac{- ( 8 a + 12 b ) \pm ( 8 a + 12 b ) ^{2} - 4 \cdot 12 a ( 4 b + 12 c )}{2 \cdot 12 a}

Vereinfache

(8 a + 12 b)^{2} - 4 \cdot 12 a (4 b + 12 c) : 4 4 a^{2} - 36 a c + 9 b^{2}

x_{1, 2} = \frac{- ( 8 a + 12 b ) \pm 4 4 a ^{2} - 36 a c + 9 b ^{2}}{2 \cdot 12 a}; a \neq = 0

Trenne die Lösungen

x_{1} = \frac{- ( 8 a + 12 b ) + 4 4 a ^{2} - 36 a c + 9 b ^{2}}{2 \cdot 12 a}, x_{2} = \frac{- ( 8 a + 12 b ) - 4 4 a ^{2} - 36 a c + 9 b ^{2}}{2 \cdot 12 a}

x = \frac{- ( 8 a + 12 b ) + 4 4 a ^{2} - 36 a c + 9 b ^{2}}{2 \cdot 12 a} : \frac{- 2 a - 3 b + 4 a ^{2} - 36 a c + 9 b ^{2}}{6 a}

x = \frac{- ( 8 a + 12 b ) - 4 4 a ^{2} - 36 a c + 9 b ^{2}}{2 \cdot 12 a} : - \frac{2 a + 3 b + 4 a ^{2} - 36 a c + 9 b ^{2}}{6 a}

Die Lösungen für die quadratische Gleichung sind:

x = \frac{- 2 a - 3 b + 4 a ^{2} - 36 a c + 9 b ^{2}}{6 a}, x = - \frac{2 a + 3 b + 4 a ^{2} - 36 a c + 9 b ^{2}}{6 a}; a \neq = 0

- 7 x^{2} - 49 x = 0

x^{2} = - 2 x + 35

- 4 x^{2} = 5 x + 9

(x + 5)^{2} - (x + 4)^{2} = (x + 3)^{2}

3 n^{2} - 10 n + 14 = 6