Solve 3n^2 7n-1360=0

Question

Solve the equation

n = \frac{2 3 74970}{21}

Alternative Form

n \approx 4.01581

Evaluate

3 n^{2} \times 7 n - 1360 = 0

Multiply

More Steps

Evaluate

3 n^{2} \times 7 n

Multiply the terms

21 n^{2} \times n

Multiply the terms with the same base by adding their exponents

21 n^{2 + 1}

Add the numbers

21 n^{3}

21 n^{3} - 1360 = 0

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

21 n^{3} = 0 + 1360

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

21 n^{3} = 1360

Divide both sides

\frac{21 n ^{3}}{21} = \frac{1360}{21}

Divide the numbers

n^{3} = \frac{1360}{21}

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

3 n^{3} = 3 \frac{1360}{21}

Calculate

n = 3 \frac{1360}{21}

Solution

More Steps

Evaluate

3 \frac{1360}{21}

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

\frac{3 1360}{3 21}

Simplify the radical expression

More Steps

Evaluate

31360

Write the expression as a product where the root of one of the factors can be evaluated

3 8 \times 170

Write the number in exponential form with the base of 2

3 2^{3} \times 170

The root of a product is equal to the product of the roots of each factor

3 2^{3} \times 3170

Reduce the index of the radical and exponent with 3

23170

\frac{2 3 170}{3 21}

Multiply by the Conjugate

\frac{2 3 170 \times 3 2 1 ^{2}}{3 21 \times 3 2 1 ^{2}}

Simplify

\frac{2 3 170 \times 3 441}{3 21 \times 3 2 1 ^{2}}

Multiply the numbers

More Steps

Evaluate

3170 \times 3441

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

3 170 \times 441

Calculate the product

374970

\frac{2 3 74970}{3 21 \times 3 2 1 ^{2}}

Multiply the numbers

More Steps

Evaluate

321 \times 3 2 1^{2}

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

3 21 \times 2 1^{2}

Calculate the product

3 2 1^{3}

Reduce the index of the radical and exponent with 3

21

\frac{2 3 74970}{21}

n = \frac{2 3 74970}{21}

Alternative Form

n \approx 4.01581

Show Solution