Solve 24x^2 14x-24=0

Question

Solve the equation

x = \frac{3 196}{14}

Alternative Form

x \approx 0.414913

Evaluate

24 x^{2} \times 14 x - 24 = 0

Multiply

More Steps

Evaluate

24 x^{2} \times 14 x

Multiply the terms

336 x^{2} \times x

Multiply the terms with the same base by adding their exponents

336 x^{2 + 1}

Add the numbers

336 x^{3}

336 x^{3} - 24 = 0

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

336 x^{3} = 0 + 24

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

336 x^{3} = 24

Divide both sides

\frac{336 x ^{3}}{336} = \frac{24}{336}

Divide the numbers

x^{3} = \frac{24}{336}

Cancel out the common factor 24

x^{3} = \frac{1}{14}

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

3 x^{3} = 3 \frac{1}{14}

Calculate

x = 3 \frac{1}{14}

Solution

More Steps

Evaluate

3 \frac{1}{14}

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

\frac{3 1}{3 14}

Simplify the radical expression

\frac{1}{3 14}

Multiply by the Conjugate

\frac{3 1 4 ^{2}}{3 14 \times 3 1 4 ^{2}}

Simplify

\frac{3 196}{3 14 \times 3 1 4 ^{2}}

Multiply the numbers

More Steps

Evaluate

314 \times 3 1 4^{2}

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

3 14 \times 1 4^{2}

Calculate the product

3 1 4^{3}

Reduce the index of the radical and exponent with 3

14

\frac{3 196}{14}

x = \frac{3 196}{14}

Alternative Form

x \approx 0.414913

Show Solution