Solve x-6/7x^3=x-6/5x-1

Question

Solve the equation(The real numbers system)

x \approx 1.479395

Evaluate

x - \frac{6}{7} x^{3} = x - \frac{6}{5} x - 1

Evaluate

More Steps

Evaluate

x - \frac{6}{5} x

Collect like terms by calculating the sum or difference of their coefficients

(1 - \frac{6}{5}) x

Subtract the numbers

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Evaluate

1 - \frac{6}{5}

Reduce fractions to a common denominator

\frac{5}{5} - \frac{6}{5}

Write all numerators above the common denominator

\frac{5 - 6}{5}

Subtract the numbers

\frac{- 1}{5}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

- \frac{1}{5}

- \frac{1}{5} x

x - \frac{6}{7} x^{3} = - \frac{1}{5} x - 1

Move the expression to the left side

x - \frac{6}{7} x^{3} - (- \frac{1}{5} x - 1) = 0

Subtract the terms

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Evaluate

x - \frac{6}{7} x^{3} - (- \frac{1}{5} x - 1)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

x - \frac{6}{7} x^{3} + \frac{1}{5} x + 1

Add the terms

More Steps

Evaluate

x + \frac{1}{5} x

Collect like terms by calculating the sum or difference of their coefficients

(1 + \frac{1}{5}) x

Add the numbers

\frac{6}{5} x

\frac{6}{5} x - \frac{6}{7} x^{3} + 1

\frac{6}{5} x - \frac{6}{7} x^{3} + 1 = 0

Factor the expression

\frac{1}{35} (42 x - 30 x^{3} + 35) = 0

Divide both sides

42 x - 30 x^{3} + 35 = 0

Solution

x \approx 1.479395

Show Solution

Solve the equation(The complex numbers system)

x_{1} \approx - 0.739698 - 0.491384 i, x_{2} \approx - 0.739698 + 0.491384 i, x_{3} \approx 1.479395

Evaluate

x - \frac{6}{7} x^{3} = x - \frac{6}{5} x - 1

Subtract the terms

More Steps

Evaluate

x - \frac{6}{5} x

Collect like terms by calculating the sum or difference of their coefficients

(1 - \frac{6}{5}) x

Subtract the numbers

More Steps

Evaluate

1 - \frac{6}{5}

Reduce fractions to a common denominator

\frac{5}{5} - \frac{6}{5}

Write all numerators above the common denominator

\frac{5 - 6}{5}

Subtract the numbers

\frac{- 1}{5}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

- \frac{1}{5}

- \frac{1}{5} x

x - \frac{6}{7} x^{3} = - \frac{1}{5} x - 1

Move the expression to the left side

x - \frac{6}{7} x^{3} - (- \frac{1}{5} x - 1) = 0

Subtract the terms

More Steps

Evaluate

x - \frac{6}{7} x^{3} - (- \frac{1}{5} x - 1)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

x - \frac{6}{7} x^{3} + \frac{1}{5} x + 1

Add the terms

More Steps

Evaluate

x + \frac{1}{5} x

Collect like terms by calculating the sum or difference of their coefficients

(1 + \frac{1}{5}) x

Add the numbers

\frac{6}{5} x

\frac{6}{5} x - \frac{6}{7} x^{3} + 1

\frac{6}{5} x - \frac{6}{7} x^{3} + 1 = 0

Factor the expression

\frac{1}{35} (42 x - 30 x^{3} + 35) = 0

Divide both sides

42 x - 30 x^{3} + 35 = 0

Calculate

x \approx 1.479395 x \approx - 0.739698 + 0.491384 i x \approx - 0.739698 - 0.491384 i

Solution

x_{1} \approx - 0.739698 - 0.491384 i, x_{2} \approx - 0.739698 + 0.491384 i, x_{3} \approx 1.479395

Show Solution

Solve the equation(The real numbers system)

Solve the equation(The complex numbers system)

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