[tex]3x(x + 1) > {x}^{2} + x + 24[/tex]
[tex] {3x}^{2} + 3x > {x}^{2} + x + 24[/tex]
[tex] {3x}^{2} - {x}^{2} + 3x - x - 24 > 0[/tex]
[tex] {2x}^{2} + 2x - 24 > 0 | \div 2[/tex]
[tex] {x}^{2} + x - 12 > 0[/tex]
∆
=
[tex] {b}^{2} - 4ac = {1}^{2} - 4 \times 1 \times ( - 12) = 1 - ( - 48) = 1 + 48 = 49[/tex]
√∆=7
[tex] x_{1} = \frac{ - b - \sqrt{∆} }{2a} = \frac{ - 1 - 7}{2 \times 1} = \frac{ - 8}{2} = - 4[/tex]
[tex] x_{2} = \frac{ - b + \sqrt{∆} }{2a} = \frac{ - 1 + 7}{2 \times 1} = \frac{6}{2} = 3[/tex]
[tex]x€( - 4;3)[/tex]
