Solve for $x$ \[ \begin{array}{c} x^{2}-5 x-24=0 \\ x=[?], \square \end{array} \] Enter the smallest solution first. Remember the quadratic formula: $x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$ Enter

Step 1 ：The given equation is a quadratic equation. The general form of a quadratic equation is \(ax^2 + bx + c = 0\). In this case, \(a = 1\), \(b = -5\), and \(c = -24\).

Step 2 ：We can solve for \(x\) using the quadratic formula, which is \(x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}\).

Step 3 ：Substitute \(a = 1\), \(b = -5\), and \(c = -24\) into the quadratic formula.

Step 4 ：Calculate the discriminant \(D = b^{2}-4 a c = 121\).

Step 5 ：Solve for \(x1 = \frac{-(-5) - \sqrt{121}}{2*1} = -3.0\) and \(x2 = \frac{-(-5) + \sqrt{121}}{2*1} = 8.0\).

Step 6 ：The solutions to the equation are \(x = -3\) and \(x = 8\). Since the question asks for the smallest solution first, the final answer is \(\boxed{-3, 8}\).