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[tex]1008= n(48n-1)[/tex]
[tex]1008= 48 {n}^{2} - n[/tex]
[tex] - 48 {n}^{2} + n + 1008 = 0[/tex]
[tex] - (48 {n}^{2} - n - 1008) = 0[/tex]
[tex]48 {n}^{2} - n - 1008 = 0[/tex]
[tex]n = \frac{ - b \: ± \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]
[tex]n = \frac{ - ( - 1) \: ± \sqrt{ {( - 1)}^{2} - 4 \times 48( - 1008)} }{2 \times 48} [/tex]
[tex]n = \frac{ - 1 \: ± \sqrt{193537} }{96} [/tex]
[tex]n = \frac{ 1 \: + \sqrt{193537} }{96} [/tex]
[tex]n = \frac{ 1 \: - \sqrt{193537} }{96} [/tex]
[tex]n = \frac{ - 1 \: ± \sqrt{193537} }{96} [/tex]