Solve 3y^2 10y-9=0

Question

Solve the equation

y = \frac{3 300}{10}

Alternative Form

y \approx 0.669433

Evaluate

3 y^{2} \times 10 y - 9 = 0

Multiply

More Steps

Evaluate

3 y^{2} \times 10 y

Multiply the terms

30 y^{2} \times y

Multiply the terms with the same base by adding their exponents

30 y^{2 + 1}

Add the numbers

30 y^{3}

30 y^{3} - 9 = 0

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

30 y^{3} = 0 + 9

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

30 y^{3} = 9

Divide both sides

\frac{30 y ^{3}}{30} = \frac{9}{30}

Divide the numbers

y^{3} = \frac{9}{30}

Cancel out the common factor 3

y^{3} = \frac{3}{10}

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

3 y^{3} = 3 \frac{3}{10}

Calculate

y = 3 \frac{3}{10}

Solution

More Steps

Evaluate

3 \frac{3}{10}

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

\frac{3 3}{3 10}

Multiply by the Conjugate

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

Simplify

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

Multiply the numbers

More Steps

Evaluate

33 \times 3100

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

3 3 \times 100

Calculate the product

3300

\frac{3 300}{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{3 300}{10}

y = \frac{3 300}{10}

Alternative Form

y \approx 0.669433

Show Solution