Solve 2x^(2) 27x-80=0

Question

Solve the equation

x = \frac{2 3 5}{3}

Alternative Form

x \approx 1.139984

Evaluate

2 x^{2} \times 27 x - 80 = 0

Multiply

More Steps

Evaluate

2 x^{2} \times 27 x

Multiply the terms

54 x^{2} \times x

Multiply the terms with the same base by adding their exponents

54 x^{2 + 1}

Add the numbers

54 x^{3}

54 x^{3} - 80 = 0

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

54 x^{3} = 0 + 80

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

54 x^{3} = 80

Divide both sides

\frac{54 x ^{3}}{54} = \frac{80}{54}

Divide the numbers

x^{3} = \frac{80}{54}

Cancel out the common factor 2

x^{3} = \frac{40}{27}

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

3 x^{3} = 3 \frac{40}{27}

Calculate

x = 3 \frac{40}{27}

Solution

More Steps

Evaluate

3 \frac{40}{27}

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

\frac{3 40}{3 27}

Simplify the radical expression

More Steps

Evaluate

340

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

3 8 \times 5

Write the number in exponential form with the base of 2

3 2^{3} \times 5

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

3 2^{3} \times 35

Reduce the index of the radical and exponent with 3

235

\frac{2 3 5}{3 27}

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{2 3 5}{3}

x = \frac{2 3 5}{3}

Alternative Form

x \approx 1.139984

Show Solution