Question

Using quadratic formula solve the equation 6a2x2-7abx-3b2=0

Answer 1

6a^2x^2-9abx+2abx-3b^2
3ax(2ax-3b) +b(2ax-3b)
(3ax+b)(2ax-3b)

Answer 2

Answer:

$x=\frac{3b}{2a},\:x=-\frac{b}{3a};\quad \:a\ne \:0$

Step-by-step explanation:

The quadratic formula is given by

$x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

The given equation is $6a^2x^2-7abx-3b^2=0$

Comparing with  $ax^2+bx+C=0$

$a=6a^2,\:b=-7ab,\:c=-3b^2$

Thus, we have

$x_{1,\:2}=\frac{-\left(-7ab\right)\pm \sqrt{\left(-7ab\right)^2-4\cdot \:6a^2\left(-3b^2\right)}}{2\cdot \:6a^2}$

$=\frac{7ab\pm\sqrt{72a^2b^2+\left(7ab\right)^2}}{2\cdot \:6a^2}\\\\=\frac{7ab\pm11ab}{12a^2}\\\\x=\frac{3b}{2a},\:x=-\frac{b}{3a}$