Can anyone solve the equation above since I have found that this equation is actually having no real root based on completing the square method.
Just to confirm, it actually has no roots right, since - square root is unsolved, unless it is involved with imaginary number. Can anyone help me to solve this？
There will be no real roots for this equation, but there will be two complex conjugate roots.
Using the method of completing the square as a check:
$$\begin{align} & 2x^2 - 5x + 4 = 0\\ \implies& x^2 - \frac {5}{2}x = -2\\ \implies& x^2 - \frac {5}{2}x + \frac {25}{16} = -2 + \frac {25}{16}\\ \implies& \left(x-\frac {5}{4}\right)^2 = -\frac {7}{16}\\ \implies& x-\frac {5}{4} = \pm \frac {\sqrt 7}{4}i\\ \implies& x = \frac {5}{4} \pm \frac {\sqrt {7}}{4}i\\ \end{align}$$