(5a+10)x^2+3ax+48=6x

Lösung

(5 a + 10) x^{2} + 3 a x + 48 = 6 x

x = \frac{- 3 a + 6 + 9 a ^{2} - 996 a - 1884}{2 ( 5 a + 10 )}, x = \frac{- 3 a + 6 - 9 a ^{2} - 996 a - 1884}{2 ( 5 a + 10 )}; a \neq = - 2

Schritte zur Lösung

(5 a + 10) x^{2} + 3 a x + 48 = 6 x

Verschiebe

6 x

auf die linke Seite

(5 a + 10) x^{2} + 3 a x + 48 - 6 x = 0

Schreibe in der Standard Form

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

(5 a + 10) x^{2} + (3 a - 6) x + 48 = 0

Löse mit der quadratischen Formel

x_{1, 2} = \frac{- ( 3 a - 6 ) \pm ( 3 a - 6 ) ^{2} - 4 ( 5 a + 10 ) \cdot 48}{2 ( 5 a + 10 )}

Vereinfache

(3 a - 6)^{2} - 4 (5 a + 10) \cdot 48 : 9 a^{2} - 996 a - 1884

x_{1, 2} = \frac{- ( 3 a - 6 ) \pm 9 a ^{2} - 996 a - 1884}{2 ( 5 a + 10 )}; a \neq = - 2

Trenne die Lösungen

x_{1} = \frac{- ( 3 a - 6 ) + 9 a ^{2} - 996 a - 1884}{2 ( 5 a + 10 )}, x_{2} = \frac{- ( 3 a - 6 ) - 9 a ^{2} - 996 a - 1884}{2 ( 5 a + 10 )}

x = \frac{- ( 3 a - 6 ) + 9 a ^{2} - 996 a - 1884}{2 ( 5 a + 10 )} : \frac{- 3 a + 6 + 9 a ^{2} - 996 a - 1884}{2 ( 5 a + 10 )}

x = \frac{- ( 3 a - 6 ) - 9 a ^{2} - 996 a - 1884}{2 ( 5 a + 10 )} : \frac{- 3 a + 6 - 9 a ^{2} - 996 a - 1884}{2 ( 5 a + 10 )}

Die Lösungen für die quadratische Gleichung sind:

x = \frac{- 3 a + 6 + 9 a ^{2} - 996 a - 1884}{2 ( 5 a + 10 )}, x = \frac{- 3 a + 6 - 9 a ^{2} - 996 a - 1884}{2 ( 5 a + 10 )}; a \neq = - 2

0 = \frac{- 32 x ^{2}}{( 45 ) ^{2}} + x + 190

4 x^{2} + 12 + 9 = 0

x^{2} - \frac{11}{3} x + 2 = 0

x^{2} - 5 = x + 6

so l v e f or x, x^{2} y - 3 y - 9 x = 0