x^2-2(3m+1)x+7(2m+3)=0

Lösung

x^{2} - 2 (3 m + 1) x + 7 (2 m + 3) = 0

x = 3 m + 1 + 9 m^{2} - 8 m - 20, x = 3 m + 1 - 9 m^{2} - 8 m - 20

Schritte zur Lösung

x^{2} - 2 (3 m + 1) x + 7 (2 m + 3) = 0

Schreibe

x^{2} - 2 (3 m + 1) x + 7 (2 m + 3)

um:

x^{2} - 6 m x - 2 x + 14 m + 21

x^{2} - 6 m x - 2 x + 14 m + 21 = 0

Schreibe in der Standard Form

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

x^{2} - (6 m + 2) x + 14 m + 21 = 0

Löse mit der quadratischen Formel

x_{1, 2} = \frac{- ( - 6 m - 2 ) \pm ( - 6 m - 2 ) ^{2} - 4 \cdot 1 \cdot ( 14 m + 21 )}{2 \cdot 1}

Vereinfache

(- 6 m - 2)^{2} - 4 \cdot 1 \cdot (14 m + 21) : 2 9 m^{2} - 8 m - 20

x_{1, 2} = \frac{- ( - 6 m - 2 ) \pm 2 9 m ^{2} - 8 m - 20}{2 \cdot 1}

Trenne die Lösungen

x_{1} = \frac{- ( - 6 m - 2 ) + 2 9 m ^{2} - 8 m - 20}{2 \cdot 1}, x_{2} = \frac{- ( - 6 m - 2 ) - 2 9 m ^{2} - 8 m - 20}{2 \cdot 1}

x = \frac{- ( - 6 m - 2 ) + 2 9 m ^{2} - 8 m - 20}{2 \cdot 1} : 3 m + 1 + 9 m^{2} - 8 m - 20

x = \frac{- ( - 6 m - 2 ) - 2 9 m ^{2} - 8 m - 20}{2 \cdot 1} : 3 m + 1 - 9 m^{2} - 8 m - 20

Die Lösungen für die quadratische Gleichung sind:

x = 3 m + 1 + 9 m^{2} - 8 m - 20, x = 3 m + 1 - 9 m^{2} - 8 m - 20

f a c t or 5 x^{2} - 25 x = 0

4 x^{2} + 24 x + 227 = 0

3 x^{2} + 2 x - 4 x^{2} + 11 = 0

4 n^{2} - 720 = 0

x^{2} - 18 = x + 2