Ratkaise x^3+18x^2+45=0

$$x ^ { 3 } + 18 x ^ { 2 } + 45 = 0$$

Ratkaise muuttujan x suhteen (complex solution)

$$x=-\frac{\left(1+\sqrt{3}i\right)\left(-3\times 2^{\frac{2}{3}}\sqrt[3]{\sqrt{505}-53}i\sqrt[6]{3}-2^{\frac{2}{3}}\sqrt[3]{9\left(\sqrt{505}-53\right)}+2\times 2^{\frac{2}{3}}\sqrt[3]{9\left(-\sqrt{505}-53\right)}-12\sqrt{3}i+12\right)}{8}\approx -7,671354725-6,042228558i$$

$$x=\frac{2^{\frac{2}{3}}\sqrt[3]{9\left(\sqrt{505}-53\right)}+2^{\frac{2}{3}}\sqrt[3]{9\left(-\sqrt{505}-53\right)}-12}{2}\approx 0,06840079+10,510778488i$$

$$x=-\frac{\left(-\sqrt{3}i+1\right)\left(3\times 2^{\frac{2}{3}}\sqrt[3]{\sqrt{505}-53}i\sqrt[6]{3}-2^{\frac{2}{3}}\sqrt[3]{9\left(\sqrt{505}-53\right)}+2\times 2^{\frac{2}{3}}\sqrt[3]{9\left(-\sqrt{505}-53\right)}+12+12\sqrt{3}i\right)}{8}\approx -10,397046065-4,46854993i$$

Ratkaise muuttujan x suhteen

$$x=-\frac{2^{\frac{2}{3}}\sqrt[3]{9\sqrt{505}+477}}{2}-\frac{2^{\frac{2}{3}}\sqrt[3]{477-9\sqrt{505}}}{2}-6\approx -18,136801579$$