Solve 5/x-3/2x=x/2

$$\frac { 5 } { x } - \frac { 3 } { 2 x } = \frac { x } { 2 }$$

Solve for x

$$x=\sqrt{7}\approx 2.645751311$$

$$x=-\sqrt{7}\approx -2.645751311$$

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 2x, the least common multiple of x,2x,2.

$$2\times 5-3=xx$$

Multiply x and x to get x^{2}.

$$2\times 5-3=x^{2}$$

Multiply 2 and 5 to get 10.

$$10-3=x^{2}$$

Subtract 3 from 10 to get 7.

$$7=x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}=7$$

Take the square root of both sides of the equation.

$$x=\sqrt{7} x=-\sqrt{7}$$

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 2x, the least common multiple of x,2x,2.

$$2\times 5-3=xx$$

Multiply x and x to get x^{2}.

$$2\times 5-3=x^{2}$$

Multiply 2 and 5 to get 10.

$$10-3=x^{2}$$

Subtract 3 from 10 to get 7.

$$7=x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}=7$$

Subtract 7 from both sides.

$$x^{2}-7=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -7 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-7\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-7\right)}}{2}$$

Multiply -4 times -7.

$$x=\frac{0±\sqrt{28}}{2}$$

Take the square root of 28.

$$x=\frac{0±2\sqrt{7}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{7}}{2} when ± is plus.

$$x=\sqrt{7}$$

Now solve the equation x=\frac{0±2\sqrt{7}}{2} when ± is minus.

$$x=-\sqrt{7}$$

The equation is now solved.

$$x=\sqrt{7} x=-\sqrt{7}$$