8x^2-(m-1)x+(m-7)=0

Lösung

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

x = \frac{m - 1 + m ^{2} - 34 m + 225}{16}, x = \frac{m - 1 - m ^{2} - 34 m + 225}{16}

Schritte zur Lösung

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

Schreibe

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

um:

8 x^{2} - m x + x + m - 7

8 x^{2} - m x + x + m - 7 = 0

Schreibe in der Standard Form

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

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

Löse mit der quadratischen Formel

x_{1, 2} = \frac{- ( - m + 1 ) \pm ( - m + 1 ) ^{2} - 4 \cdot 8 ( m - 7 )}{2 \cdot 8}

Vereinfache

(- m + 1)^{2} - 4 \cdot 8 (m - 7) : m^{2} - 34 m + 225

x_{1, 2} = \frac{- ( - m + 1 ) \pm m ^{2} - 34 m + 225}{2 \cdot 8}

Trenne die Lösungen

x_{1} = \frac{- ( - m + 1 ) + m ^{2} - 34 m + 225}{2 \cdot 8}, x_{2} = \frac{- ( - m + 1 ) - m ^{2} - 34 m + 225}{2 \cdot 8}

x = \frac{- ( - m + 1 ) + m ^{2} - 34 m + 225}{2 \cdot 8} : \frac{m - 1 + m ^{2} - 34 m + 225}{16}

x = \frac{- ( - m + 1 ) - m ^{2} - 34 m + 225}{2 \cdot 8} : \frac{m - 1 - m ^{2} - 34 m + 225}{16}

Die Lösungen für die quadratische Gleichung sind:

x = \frac{m - 1 + m ^{2} - 34 m + 225}{16}, x = \frac{m - 1 - m ^{2} - 34 m + 225}{16}

5 x^{2} + 7 x - 4 = - 7 x - 1

x (2 x - 4) = (x - 2) (x - 2)

3 x^{2} - 1 = 3 - 2 x^{2}

(3 x + 2) (2 x - 1) = 0

0.3 x^{2} + 0.4 x - 1 = 0