Solve 5t^2 72t -612 =0

Question

Solve the equation

t = \frac{3 1700}{10}

Alternative Form

t \approx 1.193483

Evaluate

5 t^{2} \times 72 t - 612 = 0

Multiply

More Steps

Evaluate

5 t^{2} \times 72 t

Multiply the terms

360 t^{2} \times t

Multiply the terms with the same base by adding their exponents

360 t^{2 + 1}

Add the numbers

360 t^{3}

360 t^{3} - 612 = 0

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

360 t^{3} = 0 + 612

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

360 t^{3} = 612

Divide both sides

\frac{360 t ^{3}}{360} = \frac{612}{360}

Divide the numbers

t^{3} = \frac{612}{360}

Cancel out the common factor 36

t^{3} = \frac{17}{10}

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

3 t^{3} = 3 \frac{17}{10}

Calculate

t = 3 \frac{17}{10}

Solution

More Steps

Evaluate

3 \frac{17}{10}

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

\frac{3 17}{3 10}

Multiply by the Conjugate

\frac{3 17 \times 3 1 0 ^{2}}{3 10 \times 3 1 0 ^{2}}

Simplify

\frac{3 17 \times 3 100}{3 10 \times 3 1 0 ^{2}}

Multiply the numbers

More Steps

Evaluate

317 \times 3100

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

3 17 \times 100

Calculate the product

31700

\frac{3 1700}{3 10 \times 3 1 0 ^{2}}

Multiply the numbers

More Steps

Evaluate

310 \times 3 1 0^{2}

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

3 10 \times 1 0^{2}

Calculate the product

3 1 0^{3}

Reduce the index of the radical and exponent with 3

10

\frac{3 1700}{10}

t = \frac{3 1700}{10}

Alternative Form

t \approx 1.193483

Show Solution