Solve 2x^2 13x-3 =0

Question

Solve the equation

x = \frac{3 2028}{26}

Alternative Form

x \approx 0.486836

Evaluate

2 x^{2} \times 13 x - 3 = 0

Multiply

More Steps

Evaluate

2 x^{2} \times 13 x

Multiply the terms

26 x^{2} \times x

Multiply the terms with the same base by adding their exponents

26 x^{2 + 1}

Add the numbers

26 x^{3}

26 x^{3} - 3 = 0

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

26 x^{3} = 0 + 3

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

26 x^{3} = 3

Divide both sides

\frac{26 x ^{3}}{26} = \frac{3}{26}

Divide the numbers

x^{3} = \frac{3}{26}

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

3 x^{3} = 3 \frac{3}{26}

Calculate

x = 3 \frac{3}{26}

Solution

More Steps

Evaluate

3 \frac{3}{26}

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

\frac{3 3}{3 26}

Multiply by the Conjugate

\frac{3 3 \times 3 2 6 ^{2}}{3 26 \times 3 2 6 ^{2}}

Simplify

\frac{3 3 \times 3 676}{3 26 \times 3 2 6 ^{2}}

Multiply the numbers

More Steps

Evaluate

33 \times 3676

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

3 3 \times 676

Calculate the product

32028

\frac{3 2028}{3 26 \times 3 2 6 ^{2}}

Multiply the numbers

More Steps

Evaluate

326 \times 3 2 6^{2}

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

3 26 \times 2 6^{2}

Calculate the product

3 2 6^{3}

Reduce the index of the radical and exponent with 3

26

\frac{3 2028}{26}

x = \frac{3 2028}{26}

Alternative Form

x \approx 0.486836

Show Solution