The value of x is [tex]\frac{3a}{4b}[/tex] and [tex]-\frac{2b}{3a}[/tex]
Explanation:
The expression is [tex]12abx^{2} -(9a^{2} -8b^{2} )x-6ab=0[/tex]
Multiplying the term x withing the bracket, we get,
[tex]12abx^{2} -9a^{2} x+8b^{2} x-6ab=0[/tex]
Grouping the terms, we have,
[tex](12abx^{2} -9a^{2} x)+(8b^{2} x-6ab)=0[/tex]
Taking out the common terms in each bracket, we get,
[tex]3ax(4bx -3a)+2b(4bx-3a)=0[/tex]
Simplifying, we get,
[tex](3ax+2b)(4bx -3a)=0[/tex]
Equating each term to zero, we get,
[tex]\begin{aligned}3 a x+2 b &=0 \\3 a x &=-2 b \\x &=-\frac{2 b}{3 a}\end{aligned}[/tex] and [tex]\begin{aligned}4 b x-3 a &=0 \\4 b x &=3 a \\x &=\frac{3 a}{4 b}\end{aligned}[/tex]
Hence, the values of x is [tex]\frac{3a}{4b}[/tex] and [tex]-\frac{2b}{3a}[/tex]
