$$4n^{2}+10n-2100=0$$

$$n=\frac{-10±\sqrt{10^{2}-4\times 4\left(-2100\right)}}{2\times 4}$$

$$n=\frac{-10±\sqrt{100-4\times 4\left(-2100\right)}}{2\times 4}$$

$$n=\frac{-10±\sqrt{100-16\left(-2100\right)}}{2\times 4}$$

$$n=\frac{-10±\sqrt{100+33600}}{2\times 4}$$

$$n=\frac{-10±\sqrt{33700}}{2\times 4}$$

$$n=\frac{-10±10\sqrt{337}}{2\times 4}$$

$$n=\frac{-10±10\sqrt{337}}{8}$$

$$n=\frac{10\sqrt{337}-10}{8}$$

$$n=\frac{5\sqrt{337}-5}{4}$$

$$n=\frac{-10\sqrt{337}-10}{8}$$

$$n=\frac{-5\sqrt{337}-5}{4}$$

$$n=\frac{5\sqrt{337}-5}{4}$$ $$n=\frac{-5\sqrt{337}-5}{4}$$

$$4n^{2}+10n-2100=0$$

$$4n^{2}+10n-2100-\left(-2100\right)=-\left(-2100\right)$$

$$4n^{2}+10n=-\left(-2100\right)$$

$$4n^{2}+10n=2100$$

$$\frac{4n^{2}+10n}{4}=\frac{2100}{4}$$

$$n^{2}+\frac{10}{4}n=\frac{2100}{4}$$

$$n^{2}+\frac{5}{2}n=\frac{2100}{4}$$

$$n^{2}+\frac{5}{2}n=525$$

$$n^{2}+\frac{5}{2}n+\left(\frac{5}{4}\right)^{2}=525+\left(\frac{5}{4}\right)^{2}$$

$$n^{2}+\frac{5}{2}n+\frac{25}{16}=525+\frac{25}{16}$$

$$n^{2}+\frac{5}{2}n+\frac{25}{16}=\frac{8425}{16}$$

$$\left(n+\frac{5}{4}\right)^{2}=\frac{8425}{16}$$

$$\sqrt{\left(n+\frac{5}{4}\right)^{2}}=\sqrt{\frac{8425}{16}}$$

$$n+\frac{5}{4}=\frac{5\sqrt{337}}{4}$$ $$n+\frac{5}{4}=-\frac{5\sqrt{337}}{4}$$

$$n=\frac{5\sqrt{337}-5}{4}$$ $$n=\frac{-5\sqrt{337}-5}{4}$$

$$x ^ 2 +\frac{5}{2}x -525 = 0$$

$$r + s = -\frac{5}{2} $$ $$ rs = -525$$

$$r = -\frac{5}{4} - u$$ $$s = -\frac{5}{4} + u$$

$$(-\frac{5}{4} - u) (-\frac{5}{4} + u) = -525$$

$$\frac{25}{16} - u^2 = -525$$

$$-u^2 = -525-\frac{25}{16} = -\frac{8425}{16}$$

$$u^2 = \frac{8425}{16}$$ $$u = \pm\sqrt{\frac{8425}{16}} = \pm \frac{\sqrt{8425}}{4} $$

$$r =-\frac{5}{4} - \frac{\sqrt{8425}}{4} = -24.197$$ $$s = -\frac{5}{4} + \frac{\sqrt{8425}}{4} = 21.697$$