Answer
The solution of the equation is $\left\{ \underline{\frac{2+\sqrt{3}i}{2},\frac{2-\sqrt{3}i}{2}} \right\}$
Work Step by Step
Represent the provided equation in standard form as shown below:
$4{{x}^{2}}-8x+7=0$
The roots of the quadratic equation $ a{{x}^{2}}+bx+c=0$ are given by the quadratic formula
$ x=\frac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}$
Where,
$\begin{align}
& a=4 \\
& b=-8 \\
& c=7 \\
\end{align}$
Substitute the values of a, b, and c in the formula and obtain,
$\begin{align}
& x=\frac{-\left( -8 \right)\pm \sqrt{{{\left( -8 \right)}^{2}}-4\left( 4 \right)\left( 7 \right)}}{2\left( 4 \right)} \\
& x=\frac{8\pm \sqrt{-48}}{8} \\
& x=\frac{8\pm 4\sqrt{3}i}{8} \\
& x=\frac{2\pm \sqrt{3}i}{2} \\
\end{align}$.
Therefore, $ x=\frac{2+\sqrt{3}i}{2},\frac{2-\sqrt{3}i}{2}$.
Hence, the solution of the equation is $ x=\left\{ \underline{\frac{2+\sqrt{3}i}{2},\frac{2-\sqrt{3}i}{2}} \right\}$.
