Question

Solve the following for $x$: $6a^2{x}^2-7abx-3b^2=0,a\ne 0$

Answer 1

Step: Solve by factorisation

$$\begin{gathered} \Rightarrow 6a^2{x}^2-7abx-3b^2=0 \\ \Rightarrow 6a^2{x}^2-9abx+2abx-3b^2=0 \\ \Rightarrow 3ax(2ax-3b)+b(2ax-3b)=0 \\ \Rightarrow (3ax+b)(2ax-3b)=0 \\ \Rightarrow 3ax+b=0or2ax-3b=0 \\ \Rightarrow x=-\frac{b}{3a}orx=\frac{3b}{2a} \end{gathered}$$

Thus, the values of $\mathit{x}$ can be $\mathbf{-}\frac{\mathbf{b}}{\mathbf{3}\mathbf{a}}$ or $\frac{\mathbf{3}\mathbf{b}}{\mathbf{2}\mathbf{a}}$ .