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

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Solution

Given equation is :

Step 1:- $12 a b x^{2} - 9 a^{2} x + 8 b^{2} x - 6 a b = 0$

Step 2:- $3 a x (4 b x - 3 a) + 2 b (4 b x - 3 a) = 0$

$\Rightarrow$ $(4 b x - 3 a) (3 a x + 2 b) = 0$

Step 3:- 4bx – 3a = 0 or 3ax + 2b = 0

x = $\frac{3 a}{4 b}$ or 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

Given equation is : Step 1:- 12abx2–9a2x+8b2x–6ab=0 Step 2:- 3ax(4bx–3a)+2b(4bx–3a)=0 ⇒ (4bx–3a)(3ax+2b)=0 Step 3:- 4bx – 3a = 0 or 3ax + 2b = 0 x = 3a4b or x = −2b3a

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

Given equation is :

Step 1:- $12 a b x^{2} - 9 a^{2} x + 8 b^{2} x - 6 a b = 0$

Step 2:- $3 a x (4 b x - 3 a) + 2 b (4 b x - 3 a) = 0$

$\Rightarrow$ $(4 b x - 3 a) (3 a x + 2 b) = 0$

Step 3:- 4bx – 3a = 0 or 3ax + 2b = 0

x = $\frac{3 a}{4 b}$ or x = $\frac{- 2 b}{3 a}$