6x^2+x((5-2x)/3)+3x-9=0

Lösung

6 x^{2} + x (\frac{5 - 2 x}{3}) + 3 x - 9 = 0

x = \frac{- 7 + 481}{16}, x = - \frac{7 + 481}{16}

Dezimale

x = 0.93323 \dots, x = - 1.80823 \dots

Schritte zur Lösung

6 x^{2} + x (\frac{5 - 2 x}{3}) + 3 x - 9 = 0

Schreibe

6 x^{2} + x (\frac{5 - 2 x}{3}) + 3 x - 9

um:

\frac{16 x ^{2}}{3} + \frac{14 x}{3} - 9

\frac{16 x ^{2}}{3} + \frac{14 x}{3} - 9 = 0

Löse mit der quadratischen Formel

x_{1, 2} = \frac{- \frac{14}{3} \pm ( \frac{14}{3} ) ^{2} - 4 \cdot \frac{16}{3} ( - 9 )}{2 \cdot \frac{16}{3}}

(\frac{14}{3})^{2} - 4 \cdot \frac{16}{3} (- 9) = \frac{2 481}{3}

x_{1, 2} = \frac{- \frac{14}{3} \pm \frac{2 481}{3}}{2 \cdot \frac{16}{3}}

Trenne die Lösungen

x_{1} = \frac{- \frac{14}{3} + \frac{2 481}{3}}{2 \cdot \frac{16}{3}}, x_{2} = \frac{- \frac{14}{3} - \frac{2 481}{3}}{2 \cdot \frac{16}{3}}

x = \frac{- \frac{14}{3} + \frac{2 481}{3}}{2 \frac{16}{3}} : \frac{- 7 + 481}{16}

x = \frac{- \frac{14}{3} - \frac{2 481}{3}}{2 \frac{16}{3}} : - \frac{7 + 481}{16}

Die Lösungen für die quadratische Gleichung sind:

x = \frac{- 7 + 481}{16}, x = - \frac{7 + 481}{16}

4 x^{2} - 9 x - 6 = 0

- 3 x^{2} + 18 x - 27 = 0

q u a d r a t i c f or m u l a 3 x^{2} = 5 x - 3

(x^{1} + x^{2}) = 5

x^{2} + 10 x - 144 = 0