a^2x^2+a(b-c)x-bc=0

Lösung

a^{2} x^{2} + a (b - c) x - b c = 0

x = \frac{c}{a}, x = - \frac{b}{a}; a \neq = 0

Schritte zur Lösung

a^{2} x^{2} + a (b - c) x - b c = 0

Schreibe

a^{2} x^{2} + a (b - c) x - b c

um:

a^{2} x^{2} + ab x - a c x - b c

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

Schreibe in der Standard Form

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

a^{2} x^{2} + (ab - a c) x - b c = 0

Löse mit der quadratischen Formel

x_{1, 2} = \frac{- ( ab - a c ) \pm ( ab - a c ) ^{2} - 4 a ^{2} ( - b c )}{2 a ^{2}}

Vereinfache

(ab - a c)^{2} - 4 a^{2} (- b c) : a (b + c)

x_{1, 2} = \frac{- ( ab - a c ) \pm a ( b + c )}{2 a ^{2}}; a \neq = 0

Trenne die Lösungen

x_{1} = \frac{- ( ab - a c ) + a ( b + c )}{2 a ^{2}}, x_{2} = \frac{- ( ab - a c ) - a ( b + c )}{2 a ^{2}}

x = \frac{- ( ab - a c ) + a ( b + c )}{2 a ^{2}} : \frac{c}{a}

x = \frac{- ( ab - a c ) - a ( b + c )}{2 a ^{2}} : - \frac{b}{a}

Die Lösungen für die quadratische Gleichung sind:

x = \frac{c}{a}, x = - \frac{b}{a}; a \neq = 0

0 = 210 + 205.06 t - 4.9 t^{2}

- 60 = 2 (h + 7)^{2} + 4

2 x^{2} - 8 = 10

x^{2} + 6 x = 80

(x - 1)^{2} + (0 + 1)^{2} = 9