Solve 0=2x^2 13x-24

Question

Solve the equation

x = \frac{3 2028}{13}

Alternative Form

x \approx 0.973672

Evaluate

0 = 2 x^{2} \times 13 x - 24

Multiply

More Steps

Evaluate

2 x^{2} \times 13 x

Multiply the terms

26 x^{2} \times x

Multiply the terms with the same base by adding their exponents

26 x^{2 + 1}

Add the numbers

26 x^{3}

0 = 26 x^{3} - 24

Swap the sides of the equation

26 x^{3} - 24 = 0

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

26 x^{3} = 0 + 24

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

26 x^{3} = 24

Divide both sides

\frac{26 x ^{3}}{26} = \frac{24}{26}

Divide the numbers

x^{3} = \frac{24}{26}

Cancel out the common factor 2

x^{3} = \frac{12}{13}

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

3 x^{3} = 3 \frac{12}{13}

Calculate

x = 3 \frac{12}{13}

Solution

More Steps

Evaluate

3 \frac{12}{13}

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

\frac{3 12}{3 13}

Multiply by the Conjugate

\frac{3 12 \times 3 1 3 ^{2}}{3 13 \times 3 1 3 ^{2}}

Simplify

\frac{3 12 \times 3 169}{3 13 \times 3 1 3 ^{2}}

Multiply the numbers

More Steps

Evaluate

312 \times 3169

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

3 12 \times 169

Calculate the product

32028

\frac{3 2028}{3 13 \times 3 1 3 ^{2}}

Multiply the numbers

More Steps

Evaluate

313 \times 3 1 3^{2}

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

3 13 \times 1 3^{2}

Calculate the product

3 1 3^{3}

Reduce the index of the radical and exponent with 3

13

\frac{3 2028}{13}

x = \frac{3 2028}{13}

Alternative Form

x \approx 0.973672

Show Solution