4x^2-(m-3)x+5=0

Lösung

4 x^{2} - (m - 3) x + 5 = 0

x = \frac{m - 3 + m ^{2} - 6 m - 71}{8}, x = \frac{m - 3 - m ^{2} - 6 m - 71}{8}

Schritte zur Lösung

4 x^{2} - (m - 3) x + 5 = 0

Schreibe

4 x^{2} - (m - 3) x + 5

um:

4 x^{2} - m x + 3 x + 5

4 x^{2} - m x + 3 x + 5 = 0

Schreibe in der Standard Form

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

4 x^{2} + (- m + 3) x + 5 = 0

Löse mit der quadratischen Formel

x_{1, 2} = \frac{- ( - m + 3 ) \pm ( - m + 3 ) ^{2} - 4 \cdot 4 \cdot 5}{2 \cdot 4}

Vereinfache

(- m + 3)^{2} - 4 \cdot 4 \cdot 5 : m^{2} - 6 m - 71

x_{1, 2} = \frac{- ( - m + 3 ) \pm m ^{2} - 6 m - 71}{2 \cdot 4}

Trenne die Lösungen

x_{1} = \frac{- ( - m + 3 ) + m ^{2} - 6 m - 71}{2 \cdot 4}, x_{2} = \frac{- ( - m + 3 ) - m ^{2} - 6 m - 71}{2 \cdot 4}

x = \frac{- ( - m + 3 ) + m ^{2} - 6 m - 71}{2 \cdot 4} : \frac{m - 3 + m ^{2} - 6 m - 71}{8}

x = \frac{- ( - m + 3 ) - m ^{2} - 6 m - 71}{2 \cdot 4} : \frac{m - 3 - m ^{2} - 6 m - 71}{8}

Die Lösungen für die quadratische Gleichung sind:

x = \frac{m - 3 + m ^{2} - 6 m - 71}{8}, x = \frac{m - 3 - m ^{2} - 6 m - 71}{8}

(11 x + 17) (2 x - 13) = 0

3 (x + 3)^{2} = 36

5 x^{2} + 20 x + 15 = 0

3 (x - 2)^{2} + 3 = 6 x - 12

q u a d r a t i c f or m u l a 3 x^{2} - 6 x + 2 = 0