What are the solutions to the equation 10x^3=(4/3)pia^3 ?

The solutions to the equation 10x^3=(4/3)pia^3 are

Find the zeros of 10x^3=(4/3)pia^3

The zeros of 10x^3=(4/3)pia^3 are

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10 x^{3} = (\frac{4}{3}) π a^{3}

x = 3 \frac{2 π a ^{3}}{15}, x = - \frac{1 5 ^{\frac{2}{3}} 3 2 3 π a}{30} + i \frac{5 ^{\frac{2}{3}} 3 2 6 3 3 π a}{10}, x = - \frac{1 5 ^{\frac{2}{3}} 3 2 3 π a}{30} - i \frac{5 ^{\frac{2}{3}} 3 2 6 3 3 π a}{10}

Solution steps

10 x^{3} = (\frac{4}{3}) π a^{3}

Divide both sides by

10

x^{3} = \frac{2 π a ^{3}}{15}

For

x^{3} = f (a)

the solutions are

x = 3 f (a), 3 f (a) \frac{- 1 - 3 i}{2}, 3 f (a) \frac{- 1 + 3 i}{2}

x = 3 \frac{2 π a ^{3}}{15}, x = 3 \frac{2 π a ^{3}}{15} \frac{- 1 + 3 i}{2}, x = 3 \frac{2 π a ^{3}}{15} \frac{- 1 - 3 i}{2}

Simplify

3 \frac{2 π a ^{3}}{15} \frac{- 1 + 3 i}{2} : - \frac{1 5 ^{\frac{2}{3}} 3 2 3 π a}{30} + i \frac{5 ^{\frac{2}{3}} 3 2 6 3 3 π a}{10}

Simplify

3 \frac{2 π a ^{3}}{15} \frac{- 1 - 3 i}{2} : - \frac{1 5 ^{\frac{2}{3}} 3 2 3 π a}{30} - i \frac{5 ^{\frac{2}{3}} 3 2 6 3 3 π a}{10}

x = 3 \frac{2 π a ^{3}}{15}, x = - \frac{1 5 ^{\frac{2}{3}} 3 2 3 π a}{30} + i \frac{5 ^{\frac{2}{3}} 3 2 6 3 3 π a}{10}, x = - \frac{1 5 ^{\frac{2}{3}} 3 2 3 π a}{30} - i \frac{5 ^{\frac{2}{3}} 3 2 6 3 3 π a}{10}

x^{4} - 28 x^{3} + 288 x^{2} - 1116 x + 1296 = 0

5 x^{4} + 1 = 0

2 x^{3} - 3 x^{2} - 12 x + 3 = 0

x^{3} - 2 x^{2} + 16

x^{3} + 6 x^{2} + 12 x + 7 = 0

What are the solutions to the equation 10x^3=(4/3)pia^3 ?
The solutions to the equation 10x^3=(4/3)pia^3 are
Find the zeros of 10x^3=(4/3)pia^3
The zeros of 10x^3=(4/3)pia^3 are