Solve 2x^2 3x-20=0

Question

Solve the equation

x = \frac{3 90}{3}

Alternative Form

x \approx 1.493802

Evaluate

2 x^{2} \times 3 x - 20 = 0

Multiply

More Steps

Evaluate

2 x^{2} \times 3 x

Multiply the terms

6 x^{2} \times x

Multiply the terms with the same base by adding their exponents

6 x^{2 + 1}

Add the numbers

6 x^{3}

6 x^{3} - 20 = 0

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

6 x^{3} = 0 + 20

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

6 x^{3} = 20

Divide both sides

\frac{6 x ^{3}}{6} = \frac{20}{6}

Divide the numbers

x^{3} = \frac{20}{6}

Cancel out the common factor 2

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

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

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

Calculate

x = 3 \frac{10}{3}

Solution

More Steps

Evaluate

3 \frac{10}{3}

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

\frac{3 10}{3 3}

Multiply by the Conjugate

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

Simplify

\frac{3 10 \times 3 9}{3 3 \times 3 3 ^{2}}

Multiply the numbers

More Steps

Evaluate

310 \times 39

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

3 10 \times 9

Calculate the product

390

\frac{3 90}{3 3 \times 3 3 ^{2}}

Multiply the numbers

More Steps

Evaluate

33 \times 3 3^{2}

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

3 3 \times 3^{2}

Calculate the product

3 3^{3}

Reduce the index of the radical and exponent with 3

3

\frac{3 90}{3}

x = \frac{3 90}{3}

Alternative Form

x \approx 1.493802

Show Solution