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

Lösung

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

x = \frac{- m + 2 + 13 m ^{2} - 8 m + 4}{2 m}, x = \frac{- m + 2 - 13 m ^{2} - 8 m + 4}{2 m}; m \neq = 0

Schritte zur Lösung

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

Schreibe

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

um:

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

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

Schreibe in der Standard Form

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

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

Löse mit der quadratischen Formel

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

Vereinfache

(m - 2)^{2} - 4 m (- 3 m + 1) : 13 m^{2} - 8 m + 4

x_{1, 2} = \frac{- ( m - 2 ) \pm 13 m ^{2} - 8 m + 4}{2 m}; m \neq = 0

Trenne die Lösungen

x_{1} = \frac{- ( m - 2 ) + 13 m ^{2} - 8 m + 4}{2 m}, x_{2} = \frac{- ( m - 2 ) - 13 m ^{2} - 8 m + 4}{2 m}

x = \frac{- ( m - 2 ) + 13 m ^{2} - 8 m + 4}{2 m} : \frac{- m + 2 + 13 m ^{2} - 8 m + 4}{2 m}

x = \frac{- ( m - 2 ) - 13 m ^{2} - 8 m + 4}{2 m} : \frac{- m + 2 - 13 m ^{2} - 8 m + 4}{2 m}

Die Lösungen für die quadratische Gleichung sind:

x = \frac{- m + 2 + 13 m ^{2} - 8 m + 4}{2 m}, x = \frac{- m + 2 - 13 m ^{2} - 8 m + 4}{2 m}; m \neq = 0

462.28 = 12.146 + 7.473 x - 0.092 x^{2}

(x + 4) (x - 2) = 3

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

5 x^{2} = 6 x - 1

3 u^{2} + 24 u = 0