Solve 6x^2 13x-5 - ScanMath

Question

Simplify the expression

Solution

78 x^{3} - 5

Evaluate

6 x^{2} \times 13 x - 5

Solution

More Steps

Evaluate

6 x^{2} \times 13 x

Multiply the terms

78 x^{2} \times x

Multiply the terms with the same base by adding their exponents

78 x^{2 + 1}

Add the numbers

78 x^{3}

78 x^{3} - 5

Show Solution

Find the roots of the algebra expression

x = \frac{3 30420}{78}

Alternative Form

x \approx 0.400214

Evaluate

6 x^{2} \times 13 x - 5

To find the roots of the expression,set the expression equal to 0

6 x^{2} \times 13 x - 5 = 0

Multiply

More Steps

Multiply the terms

6 x^{2} \times 13 x

Multiply the terms

78 x^{2} \times x

Multiply the terms with the same base by adding their exponents

78 x^{2 + 1}

Add the numbers

78 x^{3}

78 x^{3} - 5 = 0

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

78 x^{3} = 0 + 5

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

78 x^{3} = 5

Divide both sides

\frac{78 x ^{3}}{78} = \frac{5}{78}

Divide the numbers

x^{3} = \frac{5}{78}

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

3 x^{3} = 3 \frac{5}{78}

Calculate

x = 3 \frac{5}{78}

Solution

More Steps

Evaluate

3 \frac{5}{78}

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

\frac{3 5}{3 78}

Multiply by the Conjugate

\frac{3 5 \times 3 7 8 ^{2}}{3 78 \times 3 7 8 ^{2}}

Simplify

\frac{3 5 \times 3 6084}{3 78 \times 3 7 8 ^{2}}

Multiply the numbers

More Steps

Evaluate

35 \times 36084

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

3 5 \times 6084

Calculate the product

330420

\frac{3 30420}{3 78 \times 3 7 8 ^{2}}

Multiply the numbers

More Steps

Evaluate

378 \times 3 7 8^{2}

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

3 78 \times 7 8^{2}

Calculate the product

3 7 8^{3}

Reduce the index of the radical and exponent with 3

78

\frac{3 30420}{78}

x = \frac{3 30420}{78}

Alternative Form

x \approx 0.400214

Show Solution