Solve 120 = x^2 5x - 6

Question

Solve the equation

x = \frac{3 3150}{5}

Alternative Form

x \approx 2.931794

Evaluate

120 = x^{2} \times 5 x - 6

Multiply

More Steps

Evaluate

x^{2} \times 5 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 5

Add the numbers

x^{3} \times 5

Use the commutative property to reorder the terms

5 x^{3}

120 = 5 x^{3} - 6

Swap the sides of the equation

5 x^{3} - 6 = 120

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

5 x^{3} = 120 + 6

Add the numbers

5 x^{3} = 126

Divide both sides

\frac{5 x ^{3}}{5} = \frac{126}{5}

Divide the numbers

x^{3} = \frac{126}{5}

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

3 x^{3} = 3 \frac{126}{5}

Calculate

x = 3 \frac{126}{5}

Solution

More Steps

Evaluate

3 \frac{126}{5}

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

\frac{3 126}{3 5}

Multiply by the Conjugate

\frac{3 126 \times 3 5 ^{2}}{3 5 \times 3 5 ^{2}}

Simplify

\frac{3 126 \times 3 25}{3 5 \times 3 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

3126 \times 325

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

3 126 \times 25

Calculate the product

33150

\frac{3 3150}{3 5 \times 3 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

35 \times 3 5^{2}

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

3 5 \times 5^{2}

Calculate the product

3 5^{3}

Reduce the index of the radical and exponent with 3

5

\frac{3 3150}{5}

x = \frac{3 3150}{5}

Alternative Form

x \approx 2.931794

Show Solution