Solve 5/x=3/2x^3+7/8x

$$\frac { 5 } { x } = \frac { 3 } { 2 x ^ { 3 } } + \frac { 7 } { 8 x }$$

Solve for x

$$x=\frac{2\sqrt{11}}{11}\approx 0.603022689$$

$$x=-\frac{2\sqrt{11}}{11}\approx -0.603022689$$

Steps by Finding Square Root

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 8x^{3}, the least common multiple of x,2x^{3},8x.

$$8x^{2}\times 5=4\times 3+x^{2}\times 7$$

Multiply 8 and 5 to get 40.

$$40x^{2}=4\times 3+x^{2}\times 7$$

Multiply 4 and 3 to get 12.

$$40x^{2}=12+x^{2}\times 7$$

Subtract x^{2}\times 7 from both sides.

$$40x^{2}-x^{2}\times 7=12$$

Combine 40x^{2} and -x^{2}\times 7 to get 33x^{2}.

$$33x^{2}=12$$

Divide both sides by 33.

$$x^{2}=\frac{12}{33}$$

Reduce the fraction \frac{12}{33} to lowest terms by extracting and canceling out 3.

$$x^{2}=\frac{4}{11}$$

Take the square root of both sides of the equation.

$$x=\frac{2\sqrt{11}}{11} x=-\frac{2\sqrt{11}}{11}$$

Steps Using the Quadratic Formula

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 8x^{3}, the least common multiple of x,2x^{3},8x.

$$8x^{2}\times 5=4\times 3+x^{2}\times 7$$

Multiply 8 and 5 to get 40.

$$40x^{2}=4\times 3+x^{2}\times 7$$

Multiply 4 and 3 to get 12.

$$40x^{2}=12+x^{2}\times 7$$

Subtract 12 from both sides.

$$40x^{2}-12=x^{2}\times 7$$

Subtract x^{2}\times 7 from both sides.

$$40x^{2}-12-x^{2}\times 7=0$$

Combine 40x^{2} and -x^{2}\times 7 to get 33x^{2}.

$$33x^{2}-12=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 33 for a, 0 for b, and -12 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 33\left(-12\right)}}{2\times 33}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 33\left(-12\right)}}{2\times 33}$$

Multiply -4 times 33.

$$x=\frac{0±\sqrt{-132\left(-12\right)}}{2\times 33}$$

Multiply -132 times -12.

$$x=\frac{0±\sqrt{1584}}{2\times 33}$$

Take the square root of 1584.

$$x=\frac{0±12\sqrt{11}}{2\times 33}$$

Multiply 2 times 33.

$$x=\frac{0±12\sqrt{11}}{66}$$

Now solve the equation x=\frac{0±12\sqrt{11}}{66} when ± is plus.

$$x=\frac{2\sqrt{11}}{11}$$

Now solve the equation x=\frac{0±12\sqrt{11}}{66} when ± is minus.

$$x=-\frac{2\sqrt{11}}{11}$$

The equation is now solved.

$$x=\frac{2\sqrt{11}}{11} x=-\frac{2\sqrt{11}}{11}$$