Solve for $x$ : $12 a b x^{2} - (9 a^{2} - 8 b^{2}) x - 6 a b = 0$

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Solution

$12 a b x^{2} - (9 a^{2} - 8 b^{2}) x - 6 a b = 0$

$12 a b x^{2} + (- 9 a^{2} + 8 b^{2}) x - 6 a b = 0$

$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$

$x = \frac{- (- 9 a^{2} + 8 b^{2}) \pm \sqrt{(- 9 a^{2} + 8 b^{2})^{2} - 4 (12 a b) (- 6 a b)}}{2 (12 a b)}$

$x = \frac{- (- 9 a^{2} + 8 b^{2}) + \sqrt{(- 9 a^{2} + 8 b^{2})^{2} - 4 (12 a b) (- 6 a b)}}{2 (12 a b)} \Rightarrow x = \frac{3 a}{4 b}$

$x = \frac{- (- 9 a^{2} + 8 b^{2}) - \sqrt{(- 9 a^{2} + 8 b^{2})^{2} - 4 (12 a b) (- 6 a b)}}{2 (12 a b)} \Rightarrow x = \frac{- 2 b}{3 a}$

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Similar questions

12 a b x^{2} - ({9 a}^{2} - {8 b}^{2}) x - 6 a b = 0

Solve each of the following quadratic equations:
$12 a b x^{2} - (9 a^{2} - 8 b^{2}) x - 6 a b = 0$

{12 a b x}^{2} - ({9 a}^{2} - 8 b^{2}) x - 6 a b = 0

, where

a \neq 0 a n d b \neq 0

Q. Evaluate

12 a b x^{2} - (9 a^{2} - 8 b^{2}) x - 6 a b = 0

, where

a \neq 0

and

b \neq 0

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
$12 a b x^{2} - (9 a^{2} - 8 b^{2}) x - 6 a b = 0, w h e r e a \neq 0 a n d b \neq 0$

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Solve for x : 12abx2−(9a2−8b2)x−6ab=0

12abx2−(9a2−8b2)x−6ab=012abx2+(−9a2+8b2)x−6ab=0x=−b±√b2−4ac2ax=−(−9a2+8b2)±√(−9a2+8b2)2−4(12ab)(−6ab)2(12ab)x=−(−9a2+8b2)+√(−9a2+8b2)2−4(12ab)(−6ab)2(12ab)⇒x=3a4bx=−(−9a2+8b2)−√(−9a2+8b2)2−4(12ab)(−6ab)2(12ab)⇒x=−2b3a

Solve for $x$ : $12 a b x^{2} - (9 a^{2} - 8 b^{2}) x - 6 a b = 0$