[tex]a = {x}^{2} + 2x - 24 = > a - {x}^{2} - 2x + 24 = 0 = > - x {}^{2} + a - 2x + 24 = 0 = > - {x}^{2} - 2x + a + 24 = 0 = > d = ( - 2) {}^{2} - 4 \times ( - 1) \times (a + 24) = > d = 100 + 4a = > 100 + 4a > 0. \: \: 100 + 4a = 0 .\: \: 100 + 4a < 0. \: = > a > - 25. \: \: a = - 25 .\: \: a < - 25.[/tex]