Solve x ((x-1)/x)-(4/5)=4/x

Question

Solve the equation

x_{1} = \frac{9 - 481}{10}, x_{2} = \frac{9 + 481}{10}

Alternative Form

x_{1} \approx - 1.293171, x_{2} \approx 3.093171

Evaluate

x (\frac{x - 1}{x}) - \frac{4}{5} = \frac{4}{x}

Find the domain

x (\frac{x - 1}{x}) - \frac{4}{5} = \frac{4}{x}, x \neq = 0

Simplify

More Steps

x - \frac{9}{5} = \frac{4}{x}

Multiply both sides of the equation by LCD

(x - \frac{9}{5}) \times 5 x = \frac{4}{x} \times 5 x

Simplify the equation

More Steps

5 x^{2} - 9 x = \frac{4}{x} \times 5 x

Simplify the equation

More Steps

5 x^{2} - 9 x = 20

Move the expression to the left side

5 x^{2} - 9 x - 20 = 0

Substitute a= 5,b= - 9 and c= - 20 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{9 \pm ( - 9 ) ^{2} - 4 \times 5 ( - 20 )}{2 \times 5}

Simplify the expression

x = \frac{9 \pm ( - 9 ) ^{2} - 4 \times 5 ( - 20 )}{10}

Simplify the expression

More Steps

x = \frac{9 \pm 481}{10}

Separate the equation into 2 possible cases

x = \frac{9 + 481}{10} x = \frac{9 - 481}{10}

Check if the solution is in the defined range

x = \frac{9 + 481}{10} x = \frac{9 - 481}{10}, x \neq = 0

Find the intersection of the solution and the defined range

x = \frac{9 + 481}{10} x = \frac{9 - 481}{10}

Solution

x_{1} = \frac{9 - 481}{10}, x_{2} = \frac{9 + 481}{10}

Alternative Form

x_{1} \approx - 1.293171, x_{2} \approx 3.093171

Show Solution