Solve 2a^3-3a^2=-27*2

$$2 a ^ { 3 } - 3 a ^ { 2 } = - 27 \times 2$$

Solve for a (complex solution)

$$a=-\frac{\left(1+\sqrt{3}i\right)\left(-\sqrt{3}\sqrt[3]{6\sqrt{318}-107}i-\sqrt[3]{6\sqrt{318}-107}+2\sqrt[3]{-6\sqrt{318}-107}-1+\sqrt{3}i\right)}{8}\approx 1.91175238-2.590013728i$$

$$a=\frac{\sqrt[3]{6\sqrt{318}-107}+\sqrt[3]{-6\sqrt{318}-107}+1}{2}\approx 2.037141494+2.662407166i$$

$$a=-\frac{\left(-\sqrt{3}i+1\right)\left(-\sqrt{3}i-\sqrt[3]{6\sqrt{318}-107}+2\sqrt[3]{-6\sqrt{318}-107}-1+\sqrt{3}\sqrt[3]{6\sqrt{318}-107}i\right)}{8}\approx -2.448893875-0.072393439i$$

Solve for a

$$a=\frac{-\sqrt[3]{6\sqrt{318}+107}-\sqrt[3]{107-6\sqrt{318}}+1}{2}\approx -2.574282988$$