Solve 6x^213x-8=0

Question

Solve the equation

x = \frac{3 6084}{39}

Alternative Form

x \approx 0.468093

Evaluate

6 x^{2} \times 13 x - 8 = 0

Multiply

More Steps

Evaluate

6 x^{2} \times 13 x

Multiply the terms

78 x^{2} \times x

Multiply the terms with the same base by adding their exponents

78 x^{2 + 1}

Add the numbers

78 x^{3}

78 x^{3} - 8 = 0

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

78 x^{3} = 0 + 8

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

78 x^{3} = 8

Divide both sides

\frac{78 x ^{3}}{78} = \frac{8}{78}

Divide the numbers

x^{3} = \frac{8}{78}

Cancel out the common factor 2

x^{3} = \frac{4}{39}

Take the 3 -th root on both sides of the equation

3 x^{3} = 3 \frac{4}{39}

Calculate

x = 3 \frac{4}{39}

Solution

More Steps

Evaluate

3 \frac{4}{39}

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

\frac{3 4}{3 39}

Multiply by the Conjugate

\frac{3 4 \times 3 3 9 ^{2}}{3 39 \times 3 3 9 ^{2}}

Simplify

\frac{3 4 \times 3 1521}{3 39 \times 3 3 9 ^{2}}

Multiply the numbers

More Steps

Evaluate

34 \times 31521

The product of roots with the same index is equal to the root of the product

3 4 \times 1521

Calculate the product

36084

\frac{3 6084}{3 39 \times 3 3 9 ^{2}}

Multiply the numbers

More Steps

Evaluate

339 \times 3 3 9^{2}

The product of roots with the same index is equal to the root of the product

3 39 \times 3 9^{2}

Calculate the product

3 3 9^{3}

Reduce the index of the radical and exponent with 3

39

\frac{3 6084}{39}

x = \frac{3 6084}{39}

Alternative Form

x \approx 0.468093

Show Solution