Solve 6x^33 = 510x

Question

Solve the equation

x_{1} = - \frac{255}{3}, x_{2} = 0, x_{3} = \frac{255}{3}

Alternative Form

x_{1} \approx - 5.322906, x_{2} = 0, x_{3} \approx 5.322906

Evaluate

6 x^{3} \times 3 = 510 x

Multiply the terms

18 x^{3} = 510 x

Add or subtract both sides

18 x^{3} - 510 x = 0

Factor the expression

6 x (3 x^{2} - 85) = 0

Divide both sides

x (3 x^{2} - 85) = 0

Separate the equation into 2 possible cases

x = 0 3 x^{2} - 85 = 0

Solve the equation

More Steps

Evaluate

3 x^{2} - 85 = 0

Move the constant to the right-hand side and change its sign

3 x^{2} = 0 + 85

Removing 0 doesn't change the value,so remove it from the expression

3 x^{2} = 85

Divide both sides

\frac{3 x ^{2}}{3} = \frac{85}{3}

Divide the numbers

x^{2} = \frac{85}{3}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm \frac{85}{3}

Simplify the expression

More Steps

Evaluate

\frac{85}{3}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{85}{3}

Multiply by the Conjugate

\frac{85 \times 3}{3 \times 3}

Multiply the numbers

\frac{255}{3 \times 3}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{255}{3}

x = \pm \frac{255}{3}

Separate the equation into 2 possible cases

x = \frac{255}{3} x = - \frac{255}{3}

x = 0 x = \frac{255}{3} x = - \frac{255}{3}

Solution

x_{1} = - \frac{255}{3}, x_{2} = 0, x_{3} = \frac{255}{3}

Alternative Form

x_{1} \approx - 5.322906, x_{2} = 0, x_{3} \approx 5.322906

Show Solution