We denote that: \(A=x^2+x-24\)

<=> \(4A=4x^2+4x-96\)

<=> \(4A=\left(2x+1\right)^2-97\)

<=> \(4A=\left(2x+1-\sqrt{97}\right)\left(2x+1+\sqrt{97}\right)\)

<=> \(A=\dfrac{\left(2x+1-\sqrt{97}\right)\left(2x+1+\sqrt{97}\right)}{4}\)

<=> \(A=\left(x+\dfrac{1}{2}-\dfrac{\sqrt{97}}{2}\right)\left(x+\dfrac{1}{2}+\dfrac{\sqrt{97}}{2}\right)\)