Lös x^2+x^3+8=0

$${ x }^{ 2 } + { x }^{ 3 } +8=0$$

Lös ut x (complex solution)

$$x=-\frac{\left(1+\sqrt{3}i\right)\left(-\sqrt{3}\sqrt[3]{6\sqrt{330}-109}i-\sqrt{3}i-\sqrt[3]{6\sqrt{330}-109}+2\sqrt[3]{-6\sqrt{330}-109}+1\right)}{12}\approx 0,614351046-1,737368042i$$

$$x=\frac{\sqrt[3]{6\sqrt{330}-109}+\sqrt[3]{-6\sqrt{330}-109}-1}{3}\approx 0,697429337+1,785333315i$$

$$x=-\frac{\left(-\sqrt{3}i+1\right)\left(-\sqrt[3]{6\sqrt{330}-109}+2\sqrt[3]{-6\sqrt{330}-109}+1+\sqrt{3}\sqrt[3]{6\sqrt{330}-109}i+\sqrt{3}i\right)}{12}\approx -2,311780383-0,047965274i$$

Lös ut x

$$x=\frac{-\sqrt[3]{6\sqrt{330}+109}-\sqrt[3]{109-6\sqrt{330}}-1}{3}\approx -2,394858674$$