Question

What are the solutions of x^2 + 5x − 24 = 0?

Answer 1

Best bet is a graphing calculator. The solutions will be wherever the graph crosses the x-axis.
Also, you can factor that equation to find the solutions.
Find 2 numbers that will multiply to 24 and subtract to 5.
Do you know what to do from there or do you need more help?

Answer 2

x^2 + 8x - 3x - 24 = 0
x(x+8)-3(x+8)=0
(x+8)(x-3) = 0

x = -8,3