Solve 5t^2 7t - 60=0

Question

Solve the equation

t = \frac{3 588}{7}

Alternative Form

t \approx 1.196817

Evaluate

5 t^{2} \times 7 t - 60 = 0

Multiply

More Steps

Evaluate

5 t^{2} \times 7 t

Multiply the terms

35 t^{2} \times t

Multiply the terms with the same base by adding their exponents

35 t^{2 + 1}

Add the numbers

35 t^{3}

35 t^{3} - 60 = 0

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

35 t^{3} = 0 + 60

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

35 t^{3} = 60

Divide both sides

\frac{35 t ^{3}}{35} = \frac{60}{35}

Divide the numbers

t^{3} = \frac{60}{35}

Cancel out the common factor 5

t^{3} = \frac{12}{7}

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

3 t^{3} = 3 \frac{12}{7}

Calculate

t = 3 \frac{12}{7}

Solution

More Steps

Evaluate

3 \frac{12}{7}

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

\frac{3 12}{3 7}

Multiply by the Conjugate

\frac{3 12 \times 3 7 ^{2}}{3 7 \times 3 7 ^{2}}

Simplify

\frac{3 12 \times 3 49}{3 7 \times 3 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

312 \times 349

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

3 12 \times 49

Calculate the product

3588

\frac{3 588}{3 7 \times 3 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

37 \times 3 7^{2}

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

3 7 \times 7^{2}

Calculate the product

3 7^{3}

Reduce the index of the radical and exponent with 3

7

\frac{3 588}{7}

t = \frac{3 588}{7}

Alternative Form

t \approx 1.196817

Show Solution