From Förberedande kurs i matematik 1

Instead of randomly trying different values of x, it is better investigate the second-degree expression by completing the square,

\displaystyle \begin{align} 4x^{2} - 28x + 48 &= 4(x^{2} - 7x + 12)\\[5pt] &= 4\bigl((x-\tfrac{7}{2})^{2} - (\tfrac{7}{2})^{2} + 12\bigr)\\[5pt] &= 4\bigl((x-\tfrac{7}{2})^{2} - \tfrac{49}{4} + \tfrac{48}{4}\bigr)\\[5pt] &= 4\bigl((x-\tfrac{7}{2})^{2} - \tfrac{1}{4}\bigr)\\[5pt] &= 4\bigl(x - \tfrac{7}{2}\bigr)^{2}-1\,\textrm{.} \end{align}

In the expression in which the square has been completed, we see that if, e.g. \displaystyle x=7/2, then the whole expression is negative and equal to -1.

Note: All values of x between 3 and 4 give a negative value for the expression.