Answer
The solution set is\[\left\{ \frac{5\pm \sqrt{41}}{2} \right\}\].
Work Step by Step
This equation can be rewritten as\[{{x}^{2}}-5x-4=0\].
Compare the given equation with the equation\[a{{x}^{2}}+bx+c=0\]
Here,\[a=1,\,\,b=-5,\text{ and }c=-4\].
Now put these values in the quadratic formula: \[x=\frac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}\]
That is,
\[\begin{align}
& x=\frac{5\pm \sqrt{{{\left( -5 \right)}^{2}}-4\times 1\times \left( -4 \right)}}{2\times 1} \\
& =\frac{5\pm \sqrt{25+16}}{2} \\
& =\frac{5\pm \sqrt{41}}{2}
\end{align}\]
