Quadratische Gleichungen Rechner Online

Online Rechner für Quadratische Gleichungen. Der Rechner formt Gleichungen, welche nicht in der Nullform liegen, erst in die Nullform um. Abhängig davon ob die resultierende Gleichung der ABC Form oder der PQ Form entspricht wird sie anschließend mit Hilfe der dafür geeigneten Formel gelöst. Auch die beiden Spezialfälle ohne linearem bzw. absolutem Glied werden bei der Berechnung speziell berücksichtigt.

Beispiele für Quadratische Gleichungen

$x^2 + 6x + 8$

$x^2 - \frac{2}{3} - 5 = 0$

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

$12 x^2 + 1 = 7x$

$\sqrt{3} x^2 + \sqrt{3} = 6x$

Weitere Beispiele findest Du in den Quadratische Gleichungen Übungsaufgaben

Wie lautet Deine Quadratische Gleichung?

Folgendes wird berechnet:

Deine eingegebene Formel

$x{\cdot}3\left(x-3\right) = 7$

Klammern ausrechnen, vereinfachen, umschreiben

$3x^{2}-9x = 7$

Alle Werte der rechten Seite auf die linke Seite bringen (Nullform)

$3x^{2}-9x-7 = 0$

$a \neq 1$ - Berechne die quadratische Gleichung mit der ABC Formel

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Die ABC-Formel zum Berechnen

$3x^{2}-9x-7 = 0$

mit den Werten

$a = 3$ und $b = -9$ und $c = -7$

einsetzen in die ABC Formel

$x_{1,2} = \frac{-b{\pm}{\sqrt{b^2 - 4ac}}}{2a}$

Einsetzen in die ABC-Formel liefert

$x_{1,2}=\frac{-\left(-9\right) \pm \sqrt{\left(-9\right) ^2 - 4 \cdot 3 \cdot \left(-7\right) }}{2 \cdot 3}$

Wert unterhalb der Wurzel ein wenig zusammenfassen

$x_{1,2}=\frac{-\left(-9\right) \pm \sqrt{81 - \left(-84\right) }}{6}$

Wert unterhalb der Wurzel ausrechnen

$x_{1,2}=\frac{-\left(-9\right) \pm \sqrt{165}}{6}$

Wurzel ziehen

$x_{1,2}=\frac{-\left(-9\right) \pm 12.845}{6}=\frac{9 \pm 12.845}{6}$

Als Ergebnis erhält man

$x_{1}=3.6409$

$x_{2}=-0.64087$