Solve 5t^2 12t-81=0

Question

Solve the equation

t = \frac{3 3 50}{10}

Alternative Form

t \approx 1.105209

Evaluate

5 t^{2} \times 12 t - 81 = 0

Multiply

More Steps

Evaluate

5 t^{2} \times 12 t

Multiply the terms

60 t^{2} \times t

Multiply the terms with the same base by adding their exponents

60 t^{2 + 1}

Add the numbers

60 t^{3}

60 t^{3} - 81 = 0

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

60 t^{3} = 0 + 81

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

60 t^{3} = 81

Divide both sides

\frac{60 t ^{3}}{60} = \frac{81}{60}

Divide the numbers

t^{3} = \frac{81}{60}

Cancel out the common factor 3

t^{3} = \frac{27}{20}

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

3 t^{3} = 3 \frac{27}{20}

Calculate

t = 3 \frac{27}{20}

Solution

More Steps

Evaluate

3 \frac{27}{20}

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

\frac{3 27}{3 20}

Simplify the radical expression

More Steps

Evaluate

327

Write the number in exponential form with the base of 3

3 3^{3}

Reduce the index of the radical and exponent with 3

3

\frac{3}{3 20}

Multiply by the Conjugate

\frac{3 3 2 0 ^{2}}{3 20 \times 3 2 0 ^{2}}

Simplify

\frac{3 \times 2 3 50}{3 20 \times 3 2 0 ^{2}}

Multiply the numbers

\frac{6 3 50}{3 20 \times 3 2 0 ^{2}}

Multiply the numbers

More Steps

Evaluate

320 \times 3 2 0^{2}

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

3 20 \times 2 0^{2}

Calculate the product

3 2 0^{3}

Reduce the index of the radical and exponent with 3

20

\frac{6 3 50}{20}

Cancel out the common factor 2

\frac{3 3 50}{10}

t = \frac{3 3 50}{10}

Alternative Form

t \approx 1.105209

Show Solution