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

Lösung

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

x = \frac{9 m + 3 + 77 m ^{2} + 42 m + 9}{2 m}, x = \frac{9 m + 3 - 77 m ^{2} + 42 m + 9}{2 m}; m \neq = 0

Schritte zur Lösung

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

Schreibe

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

um:

m x^{2} - 9 m x - 3 x + m + 3

m x^{2} - 9 m x - 3 x + m + 3 = 0

Schreibe in der Standard Form

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

m x^{2} - (9 m + 3) x + m + 3 = 0

Löse mit der quadratischen Formel

x_{1, 2} = \frac{- ( - 9 m - 3 ) \pm ( - 9 m - 3 ) ^{2} - 4 m ( m + 3 )}{2 m}

Vereinfache

(- 9 m - 3)^{2} - 4 m (m + 3) : 77 m^{2} + 42 m + 9

x_{1, 2} = \frac{- ( - 9 m - 3 ) \pm 77 m ^{2} + 42 m + 9}{2 m}; m \neq = 0

Trenne die Lösungen

x_{1} = \frac{- ( - 9 m - 3 ) + 77 m ^{2} + 42 m + 9}{2 m}, x_{2} = \frac{- ( - 9 m - 3 ) - 77 m ^{2} + 42 m + 9}{2 m}

x = \frac{- ( - 9 m - 3 ) + 77 m ^{2} + 42 m + 9}{2 m} : \frac{9 m + 3 + 77 m ^{2} + 42 m + 9}{2 m}

x = \frac{- ( - 9 m - 3 ) - 77 m ^{2} + 42 m + 9}{2 m} : \frac{9 m + 3 - 77 m ^{2} + 42 m + 9}{2 m}

Die Lösungen für die quadratische Gleichung sind:

x = \frac{9 m + 3 + 77 m ^{2} + 42 m + 9}{2 m}, x = \frac{9 m + 3 - 77 m ^{2} + 42 m + 9}{2 m}; m \neq = 0

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

10 q^{2} - 4 q + 1 = 6 q^{2}

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

2 x^{2} + 12 x = - 3

8 x^{2} + 13 x - 6 = 0