Løs 2x^3+2x^2+41=0

$$2 x ^ { 3 } + 2 x ^ { 2 } + 41 = 0$$

Løs for x (complex solution)

$$x=-\frac{4^{\frac{2}{3}}\left(1+\sqrt{3}i\right)\left(-\sqrt{3}\sqrt[3]{3\sqrt{137145}-1111}i-\sqrt{3}\sqrt[3]{4}i-\sqrt[3]{3\sqrt{137145}-1111}+2\sqrt[3]{-3\sqrt{137145}-1111}+\sqrt[3]{4}\right)}{48}\approx 0,996187925-2,373032005i$$

$$x=\frac{4^{\frac{2}{3}}\left(\sqrt[3]{3\sqrt{137145}-1111}+\sqrt[3]{-3\sqrt{137145}-1111}-\sqrt[3]{4}\right)}{12}\approx 1,057012038+2,408148823i$$

$$x=-\frac{4^{\frac{2}{3}}\left(-\sqrt{3}i+1\right)\left(-\sqrt[3]{3\sqrt{137145}-1111}+2\sqrt[3]{-3\sqrt{137145}-1111}+\sqrt[3]{4}+\sqrt{3}\sqrt[3]{3\sqrt{137145}-1111}i+\sqrt{3}\sqrt[3]{4}i\right)}{48}\approx -3,053199963-0,035116818i$$

Løs for x

$$x=-\frac{4^{\frac{2}{3}}\sqrt[3]{3\sqrt{137145}+1111}}{12}-\frac{4^{\frac{2}{3}}\sqrt[3]{1111-3\sqrt{137145}}}{12}-\frac{1}{3}\approx -3,114024076$$