Solve for x: 12abx^2 - (9a^2 - 8b^2)x - 6ab = 0?

Answer 1

Factor by grouping.
First, remove parentheses:
12abx^2-9a^2+8b^2-6ab=0
Then factor out :3ax and 2b
3ax(4bx-3a)+2b(4bx-3a)=0
Then factor out 4bx-3a:
(3ax+2b)(4bx-3a)=0
Then set each term equal to zero to solve the equation:
1.
3ax+2b=0
3ax=-2b (subtraction of 2b from each side)
x=(-2b)/(3a) (division by 3a)
2.
4bx-3a=0
4bx=3a (add 3a (or rather subtract -3a) from each side)
x=(3a)/(4b) divide by 4b

Hence, the solution:
x=(-2b)/(3a),(3a)/(4b)

Answer 2

use the quadratic formula for solution to, Ax^2+Bx+C=0, with

A=12ab, B=-(9a^2-8b^2), C=-6ab

remember its,

x={-b +or- sqrt (b^2-4ac)} / 2a

Answer 3

here A = 12 ab , B = -(9a2-8b2) , C = -6ab

=> D2 = B2- 4 AC
= (9a2-8b2)2 -4(12ab)(-6ab)
= (9a2-8b2)2 + 288a2b2
= 81 a4 +64b4 -144a2b2 + 288a2b2
=81 a4 +64b4 +144a2b2
=>D2 = (9a2+8b2)2
=> D =(9a2+8b2) , - (9a2+8b2)

x = (-B +D) / 2A , (-B - D) / 2A
=> x = (9a2-8b2+ 9a2+8b2 )/2(12ab) ,
(9a2-8b2 -9a2-8b2 )/2(12ab)
=> x = 18 a2 /24ab , -16b2/24ab
=> x = 3a/4b , - 2b/3a Answer

Answer 4

x = 3a/4b or -2b/3a

Using A=(12ab), B= -(9a^2-8b^2),C = -6ab

x = (-B [+-] ( B^2-4AC)^(1/2))/2A

Answer 5

x= 9ba^4

Answer 6

12abx^2-9a^2x+8b^2x-6ab=0
3ax[4bx-3a]+2b[4bx-3a]=0
[3ax+2b][4bx-3a]=0
x=-2b/2a,3a/4b

Answer 7

12abx^2-9a^2x+8b^2x-6ab=0
3ax(4bx-3a)+2b(4bx-3a)=0
(4bx-3a)(3ax+2b)=0
4bx-3a=0
b=3a/4b
3ax+2b=0
x=-2b/3a

Answer 8

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