Answer
The solution set is\[\left\{ \frac{3}{2} \right\}\].
Work Step by Step
The given equation can be written as\[4{{x}^{2}}-12x+9=0\].
Compare the given equation with the equation\[a{{x}^{2}}+bx+c=0\].
Here,\[a=4,\,\,b=-12,\text{ and }c=9\].
Now put these values in the quadratic formula: \[x=\frac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}\]
That is,
\[\begin{align}
& x=\frac{12\pm \sqrt{{{\left( -12 \right)}^{2}}-4\times 4\times 9}}{2\times 4} \\
& =\frac{12\pm \sqrt{144-144}}{8} \\
& =\frac{12\pm \sqrt{0}}{8}
\end{align}\]
Hence, the solution set is\[\left\{ \frac{3}{2} \right\}\].
