Solve 8x^6+215x^3-27=0

$$8 x ^ { 6 } + 215 x ^ { 3 } - 27 = 0$$

Solve for x

$$x=-3$$

$$x=\frac{1}{2}=0.5$$

Steps Using the Quadratic Formula

Substitute t for x^{3}.

$$8t^{2}+215t-27=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Substitute 8 for a, 215 for b, and -27 for c in the quadratic formula.

$$t=\frac{-215±\sqrt{215^{2}-4\times 8\left(-27\right)}}{2\times 8}$$

Do the calculations.

$$t=\frac{-215±217}{16}$$

Solve the equation t=\frac{-215±217}{16} when ± is plus and when ± is minus.

$$t=\frac{1}{8} t=-27$$

Since x=t^{3}, the solutions are obtained by evaluating x=\sqrt[3]{t} for each t.

$$x=\frac{1}{2} x=-3$$