Answer
-2.5 and 9.5
Step-by-step explanation
Given the equation:
[tex]x^2-7x-24=0[/tex]we can solve this equation with help of the quadratic formula with the coefficients a = 1, b = -7, and c = -24, as follows:
[tex]\begin{gathered} x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ x_{1,2}=\frac{7\pm\sqrt{(-7)^2-4\cdot1\cdot(-24)}}{2\cdot1} \\ x_{1,2}=\frac{7\pm\sqrt{145}}{2} \\ x_1=\frac{7+\sqrt{145}}{2}\approx9.5 \\ x_2=\frac{7-\sqrt{145}}{2}\approx-2.5 \end{gathered}[/tex]