Answer
the solution set is\[\left\{ -\sqrt{6},\sqrt{6} \right\}\].
Work Step by Step
The given equation can be written as,\[2{{x}^{2}}-9x-3=9-9x\]
Simplify this as follows:
\[\begin{align}
& 2{{x}^{2}}-9x-3-9+9x=0 \\
& 2{{x}^{2}}-12=0
\end{align}\]
Compare the given equation with the equation,\[a{{x}^{2}}+bx+c=0\]
Here,\[a=2,b=0\text{ and }c=-12\]
Now, put these values in the quadratic formula: \[x=\frac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}\]
That is,
\[\begin{align}
& x=\frac{-0\pm \sqrt{{{0}^{2}}-4\times \left( 2 \right)\times \left( -12 \right)}}{2\times 2} \\
& =\frac{0\pm \sqrt{0+96}}{4} \\
& =\frac{0\pm 4\sqrt{6}}{4} \\
& =-\sqrt{6},\sqrt{6}
\end{align}\]
Hence, the solution set is\[\left\{ -\sqrt{6},\sqrt{6} \right\}\].
