Solve x=2+5/6x

$$x = \frac { 2 + 5 } { 6 x }$$

Solve for x

$$x = \frac{\sqrt{42}}{6} \approx 1.08012345$$

$$x = -\frac{\sqrt{42}}{6} \approx -1.08012345$$

Steps by Finding Square Root

Add 2 and 5 to get 7.

$$x=\frac{7}{6x}$$

Subtract \frac{7}{6x} from both sides.

$$x-\frac{7}{6x}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{6x}{6x}.

$$\frac{x\times 6x}{6x}-\frac{7}{6x}=0$$

Since \frac{x\times 6x}{6x} and \frac{7}{6x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x\times 6x-7}{6x}=0$$

Do the multiplications in x\times 6x-7.

$$\frac{6x^{2}-7}{6x}=0$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 6x.

$$6x^{2}-7=0$$

Add 7 to both sides. Anything plus zero gives itself.

$$6x^{2}=7$$

Divide both sides by 6.

$$x^{2}=\frac{7}{6}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{42}}{6} x=-\frac{\sqrt{42}}{6}$$

Steps Using the Quadratic Formula

Add 2 and 5 to get 7.

$$x=\frac{7}{6x}$$

Subtract \frac{7}{6x} from both sides.

$$x-\frac{7}{6x}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{6x}{6x}.

$$\frac{x\times 6x}{6x}-\frac{7}{6x}=0$$

Since \frac{x\times 6x}{6x} and \frac{7}{6x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x\times 6x-7}{6x}=0$$

Do the multiplications in x\times 6x-7.

$$\frac{6x^{2}-7}{6x}=0$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 6x.

$$6x^{2}-7=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 6 for a, 0 for b, and -7 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 6\left(-7\right)}}{2\times 6}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 6\left(-7\right)}}{2\times 6}$$

Multiply -4 times 6.

$$x=\frac{0±\sqrt{-24\left(-7\right)}}{2\times 6}$$

Multiply -24 times -7.

$$x=\frac{0±\sqrt{168}}{2\times 6}$$

Take the square root of 168.

$$x=\frac{0±2\sqrt{42}}{2\times 6}$$

Multiply 2 times 6.

$$x=\frac{0±2\sqrt{42}}{12}$$

Now solve the equation x=\frac{0±2\sqrt{42}}{12} when ± is plus.

$$x=\frac{\sqrt{42}}{6}$$

Now solve the equation x=\frac{0±2\sqrt{42}}{12} when ± is minus.

$$x=-\frac{\sqrt{42}}{6}$$

The equation is now solved.

$$x=\frac{\sqrt{42}}{6} x=-\frac{\sqrt{42}}{6}$$