Solve 6x^24x 1=9x

Question

6 x^{2} \times 4 x \times 1 = 9 x

Solve the equation

x_{1} = - \frac{6}{4}, x_{2} = 0, x_{3} = \frac{6}{4}

Alternative Form

x_{1} \approx - 0.612372, x_{2} = 0, x_{3} \approx 0.612372

Evaluate

6 x^{2} \times 4 x \times 1 = 9 x

Multiply the terms

More Steps

Evaluate

6 x^{2} \times 4 x \times 1

Rewrite the expression

6 x^{2} \times 4 x

Multiply the terms

24 x^{2} \times x

Multiply the terms with the same base by adding their exponents

24 x^{2 + 1}

Add the numbers

24 x^{3}

24 x^{3} = 9 x

Add or subtract both sides

24 x^{3} - 9 x = 0

Factor the expression

3 x (8 x^{2} - 3) = 0

Divide both sides

x (8 x^{2} - 3) = 0

Separate the equation into 2 possible cases

x = 0 8 x^{2} - 3 = 0

Solve the equation

More Steps

Evaluate

8 x^{2} - 3 = 0

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

8 x^{2} = 0 + 3

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

8 x^{2} = 3

Divide both sides

\frac{8 x ^{2}}{8} = \frac{3}{8}

Divide the numbers

x^{2} = \frac{3}{8}

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

x = \pm \frac{3}{8}

Simplify the expression

More Steps

Evaluate

\frac{3}{8}

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

\frac{3}{8}

Simplify the radical expression

\frac{3}{2 2}

Multiply by the Conjugate

\frac{3 \times 2}{2 2 \times 2}

Multiply the numbers

\frac{6}{2 2 \times 2}

Multiply the numbers

\frac{6}{4}

x = \pm \frac{6}{4}

Separate the equation into 2 possible cases

x = \frac{6}{4} x = - \frac{6}{4}

x = 0 x = \frac{6}{4} x = - \frac{6}{4}

Solution

x_{1} = - \frac{6}{4}, x_{2} = 0, x_{3} = \frac{6}{4}

Alternative Form

x_{1} \approx - 0.612372, x_{2} = 0, x_{3} \approx 0.612372

Show Solution