Question

the solutions of $x^2 - 2x - 24 = 0$ are: 8 and -3 -8 and 3 -6 and 4 6 and -4

Explanation:

Step1: Factor the quadratic equation

We need two numbers that multiply to $-24$ and add to $-2$. These numbers are $-6$ and $4$.
$x^2 - 2x - 24 = (x - 6)(x + 4) = 0$

Step2: Solve for $x$

Set each factor equal to 0 and solve.
$x - 6 = 0 \implies x = 6$
$x + 4 = 0 \implies x = -4$

Answer:

6 and -4