$$4n^{2}+20n+4200=0$$

$$n=\frac{-20±\sqrt{20^{2}-4\times 4\times 4200}}{2\times 4}$$

$$n=\frac{-20±\sqrt{400-4\times 4\times 4200}}{2\times 4}$$

$$n=\frac{-20±\sqrt{400-16\times 4200}}{2\times 4}$$

$$n=\frac{-20±\sqrt{400-67200}}{2\times 4}$$

$$n=\frac{-20±\sqrt{-66800}}{2\times 4}$$

$$n=\frac{-20±20\sqrt{167}i}{2\times 4}$$

$$n=\frac{-20±20\sqrt{167}i}{8}$$

$$n=\frac{-20+20\sqrt{167}i}{8}$$

$$n=\frac{-5+5\sqrt{167}i}{2}$$

$$n=\frac{-20\sqrt{167}i-20}{8}$$

$$n=\frac{-5\sqrt{167}i-5}{2}$$

$$n=\frac{-5+5\sqrt{167}i}{2}$$ $$n=\frac{-5\sqrt{167}i-5}{2}$$

$$4n^{2}+20n+4200=0$$

$$4n^{2}+20n+4200-4200=-4200$$

$$4n^{2}+20n=-4200$$

$$\frac{4n^{2}+20n}{4}=-\frac{4200}{4}$$

$$n^{2}+\frac{20}{4}n=-\frac{4200}{4}$$

$$n^{2}+5n=-\frac{4200}{4}$$

$$n^{2}+5n=-1050$$

$$n^{2}+5n+\left(\frac{5}{2}\right)^{2}=-1050+\left(\frac{5}{2}\right)^{2}$$

$$n^{2}+5n+\frac{25}{4}=-1050+\frac{25}{4}$$

$$n^{2}+5n+\frac{25}{4}=-\frac{4175}{4}$$

$$\left(n+\frac{5}{2}\right)^{2}=-\frac{4175}{4}$$

$$\sqrt{\left(n+\frac{5}{2}\right)^{2}}=\sqrt{-\frac{4175}{4}}$$

$$n+\frac{5}{2}=\frac{5\sqrt{167}i}{2}$$ $$n+\frac{5}{2}=-\frac{5\sqrt{167}i}{2}$$

$$n=\frac{-5+5\sqrt{167}i}{2}$$ $$n=\frac{-5\sqrt{167}i-5}{2}$$

$$x ^ 2 +5x +1050 = 0$$

$$r + s = -5 $$ $$ rs = 1050$$

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

$$(-\frac{5}{2} - u) (-\frac{5}{2} + u) = 1050$$

$$\frac{25}{4} - u^2 = 1050$$

$$-u^2 = 1050-\frac{25}{4} = \frac{4175}{4}$$

$$u^2 = -\frac{4175}{4}$$ $$u = \pm\sqrt{-\frac{4175}{4}} = \pm \frac{\sqrt{4175}}{2}i $$

$$r =-\frac{5}{2} - \frac{\sqrt{4175}}{2}i = -2.5 - 32.30711995830021i$$ $$s = -\frac{5}{2} + \frac{\sqrt{4175}}{2}i = -2.5 + 32.30711995830021i$$