Solve 6x^2 x-15=0

Question

Solve the equation

x = \frac{3 20}{2}

Alternative Form

x \approx 1.357209

Evaluate

6 x^{2} \times x - 15 = 0

Multiply

More Steps

Evaluate

6 x^{2} \times x

Multiply the terms with the same base by adding their exponents

6 x^{2 + 1}

Add the numbers

6 x^{3}

6 x^{3} - 15 = 0

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

6 x^{3} = 0 + 15

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

6 x^{3} = 15

Divide both sides

\frac{6 x ^{3}}{6} = \frac{15}{6}

Divide the numbers

x^{3} = \frac{15}{6}

Cancel out the common factor 3

x^{3} = \frac{5}{2}

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

3 x^{3} = 3 \frac{5}{2}

Calculate

x = 3 \frac{5}{2}

Solution

More Steps

Evaluate

3 \frac{5}{2}

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

\frac{3 5}{3 2}

Multiply by the Conjugate

\frac{3 5 \times 3 2 ^{2}}{3 2 \times 3 2 ^{2}}

Simplify

\frac{3 5 \times 3 4}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

35 \times 34

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

3 5 \times 4

Calculate the product

320

\frac{3 20}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

32 \times 3 2^{2}

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

3 2 \times 2^{2}

Calculate the product

3 2^{3}

Reduce the index of the radical and exponent with 3

2

\frac{3 20}{2}

x = \frac{3 20}{2}

Alternative Form

x \approx 1.357209

Show Solution