6x^2+(a-12)x-(a^2+a-6)=0

Lösung

6 x^{2} + (a - 12) x - (a^{2} + a - 6) = 0

x = \frac{a + 3}{3}, x = \frac{- a + 2}{2}

Schritte zur Lösung

6 x^{2} + (a - 12) x - (a^{2} + a - 6) = 0

Schreibe

6 x^{2} + (a - 12) x - (a^{2} + a - 6)

um:

6 x^{2} + a x - 12 x - a^{2} - a + 6

6 x^{2} + a x - 12 x - a^{2} - a + 6 = 0

Schreibe in der Standard Form

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

6 x^{2} + (a - 12) x - a^{2} - a + 6 = 0

Löse mit der quadratischen Formel

x_{1, 2} = \frac{- ( a - 12 ) \pm ( a - 12 ) ^{2} - 4 \cdot 6 ( - a ^{2} - a + 6 )}{2 \cdot 6}

Vereinfache

(a - 12)^{2} - 4 \cdot 6 (- a^{2} - a + 6) : 5 a

x_{1, 2} = \frac{- ( a - 12 ) \pm 5 a}{2 \cdot 6}

Trenne die Lösungen

x_{1} = \frac{- ( a - 12 ) + 5 a}{2 \cdot 6}, x_{2} = \frac{- ( a - 12 ) - 5 a}{2 \cdot 6}

x = \frac{- ( a - 12 ) + 5 a}{2 \cdot 6} : \frac{a + 3}{3}

x = \frac{- ( a - 12 ) - 5 a}{2 \cdot 6} : \frac{- a + 2}{2}

Die Lösungen für die quadratische Gleichung sind:

x = \frac{a + 3}{3}, x = \frac{- a + 2}{2}

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

so l v e f or x, p^{2} + q^{2} = x^{2} + y^{2}

so l v e f or y, x^{3} - x \cdot y^{2} + 3 y^{2} + 2 = 0

so l v e f or x, f (1 + x) (x - 5) = y

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