Solve 8/x=x/6

$$\frac { 8 } { x } = \frac { x } { 6 }$$

Solve for x

$$x=4\sqrt{3}\approx 6.92820323$$

$$x=-4\sqrt{3}\approx -6.92820323$$

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 6x, the least common multiple of x,6.

$$6\times 8=xx$$

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

$$6\times 8=x^{2}$$

Multiply 6 and 8 to get 48.

$$48=x^{2}$$

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

$$x^{2}=48$$

Take the square root of both sides of the equation.

$$x=4\sqrt{3} x=-4\sqrt{3}$$

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 6x, the least common multiple of x,6.

$$6\times 8=xx$$

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

$$6\times 8=x^{2}$$

Multiply 6 and 8 to get 48.

$$48=x^{2}$$

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

$$x^{2}=48$$

Subtract 48 from both sides.

$$x^{2}-48=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -48 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-48\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-48\right)}}{2}$$

Multiply -4 times -48.

$$x=\frac{0±\sqrt{192}}{2}$$

Take the square root of 192.

$$x=\frac{0±8\sqrt{3}}{2}$$

Now solve the equation x=\frac{0±8\sqrt{3}}{2} when ± is plus.

$$x=4\sqrt{3}$$

Now solve the equation x=\frac{0±8\sqrt{3}}{2} when ± is minus.

$$x=-4\sqrt{3}$$

The equation is now solved.

$$x=4\sqrt{3} x=-4\sqrt{3}$$