Here is number 7:
[tex] {x}^{2} - 11x = - 24 \\ {x}^{2} - 11x + 24 = 0 \\ (x - 3)(x - 8) = 0 \\ x = 3 \: and \: 8[/tex]
Here is number 8:
[tex]3 {x}^{3} + 3 {x}^{2} = 27x \\ 3 {x}^{3} + 3 {x}^{2} - 27x = 0 \\ 3x( {x }^{2} + x - 9) = 0 \\ x = 0 \: and \: two \: more \: solutions \: shown \: below.[/tex]
Use the quadratic formula to find the other two solutions:
[tex]x = \frac{ - 1 + - \sqrt{ {1}^{2} - 4(1)( - 9) } }{2(1)} \\ x = \frac{ - 1 + \sqrt{37} }{2} \\ x = \frac{ - 1 - \sqrt{37} }{2} [/tex]
