Mathe Helferlein
Mathematik (endlich) verstehen
Quadratische Gleichungen
Übersicht Online Rechner Übungsaufgaben ABC-Formel ABC-Formel Rechner ABC-Formel Übungsaufgaben PQ-Formel PQ-Formel Rechner PQ-Formel Übungsaufgaben

Binomische Formeln
Binomische Formeln Rechner Übungsaufgaben

PQ Formel Rechner - mit Brüchen und Gleichungen

Online Rechner für die PQ Formel. Es können beliebige Gleichungen eingegeben werden welche anschießend in eine für die PQ Formel anwendbare Form umgerechnet werden. Für die Lösung wird hierbei in allen Fällen die PQ Formel angewendet. Die Rechenschritte zur Lösung werden hierbei mit angezeigt.

Beispiele für den PQ-Formel Online Rechner:
$x^2 + 6x + 8$
$x^2 - \frac{2}{3} - 5 = 0$
$-(3x+3)(2x+4)$
$12 x^2 + 1 = 7x$
$\sqrt{3} x^2 + \sqrt{3} = 6x$

Weitere Beispiele findest Du in den PQ Formel Übungsaufgaben


Wie lautet Deine PQ-Formel?

Folgendes wird berechnet:



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Deine eingegebene Formel

$9x^{2}+18x-72 = 0$


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Auf Normalform bringen (Term vor $x^2$ muss 1 sein)

$\frac{9}{9}x^2 + \frac{18}{9}x-\frac{72}{9} = 0$

Die PQ-Formel zum Berechnen

$x^2+2x-8 = 0$

mit den Werten

$p = 2$ und $q = -8$

einsetzen in die PQ Formel

$x_{1,2}=-{\frac{p}{2} \pm \sqrt{\left(\frac{p}{2}\right)^2-q}}$

Einsetzen in die PQ-Formel liefert

$x_{1,2}=-\frac{2}{2} \pm \sqrt{\left(\frac{2}2\right)^2-(-8)}$

Nach Möglichkeit $-\frac{p}{2}$ vereinfachen, Quadrat in der Wurzel ausrechnen

$x_{1,2}=-1 \pm \sqrt{1-(-8)}$

Wert in der Wurzel ausrechnen

$x_{1,2}=-1\pm \sqrt{9}$

Wurzel ziehen

$x_{1,2}=-1\pm 3$

Als Ergebnis erhält man

$x_{1}=2$

$x_{2}=-4$