Solve 1+26/6^2-x^2-x/6x+6^2-x/6x-6^2=0

$$1 + \frac { 26 } { 6 ^ { 2 } - x ^ { 2 } } - \frac { x } { 6 x + 6 ^ { 2 } } - \frac { x } { 6 x - 6 ^ { 2 } } = 0$$

Solve for x

$$x=\sqrt{93}\approx 9.643650761$$

$$x=-\sqrt{93}\approx -9.643650761$$

Steps by Finding Square Root

Variable x cannot be equal to any of the values -6,6 since division by zero is not defined. Multiply both sides of the equation by 6\left(x-6\right)\left(x+6\right), the least common multiple of 6^{2}-x^{2},6x+6^{2},6x-6^{2}.

$$6\left(x-6\right)\left(x+6\right)-6\times 26-\left(x-6\right)x-\left(x+6\right)x=0$$

Use the distributive property to multiply 6 by x-6.

$$\left(6x-36\right)\left(x+6\right)-6\times 26-\left(x-6\right)x-\left(x+6\right)x=0$$

Use the distributive property to multiply 6x-36 by x+6 and combine like terms.

$$6x^{2}-216-6\times 26-\left(x-6\right)x-\left(x+6\right)x=0$$

Multiply -6 and 26 to get -156.

$$6x^{2}-216-156-\left(x-6\right)x-\left(x+6\right)x=0$$

Subtract 156 from -216 to get -372.

$$6x^{2}-372-\left(x-6\right)x-\left(x+6\right)x=0$$

Use the distributive property to multiply x-6 by x.

$$6x^{2}-372-\left(x^{2}-6x\right)-\left(x+6\right)x=0$$

To find the opposite of x^{2}-6x, find the opposite of each term.

$$6x^{2}-372-x^{2}+6x-\left(x+6\right)x=0$$

Combine 6x^{2} and -x^{2} to get 5x^{2}.

$$5x^{2}-372+6x-\left(x+6\right)x=0$$

Use the distributive property to multiply x+6 by x.

$$5x^{2}-372+6x-\left(x^{2}+6x\right)=0$$

To find the opposite of x^{2}+6x, find the opposite of each term.

$$5x^{2}-372+6x-x^{2}-6x=0$$

Combine 5x^{2} and -x^{2} to get 4x^{2}.

$$4x^{2}-372+6x-6x=0$$

Combine 6x and -6x to get 0.

$$4x^{2}-372=0$$

Add 372 to both sides. Anything plus zero gives itself.

$$4x^{2}=372$$

Divide both sides by 4.

$$x^{2}=\frac{372}{4}$$

Divide 372 by 4 to get 93.

$$x^{2}=93$$

Take the square root of both sides of the equation.

$$x=\sqrt{93} x=-\sqrt{93}$$

Steps Using the Quadratic Formula

Variable x cannot be equal to any of the values -6,6 since division by zero is not defined. Multiply both sides of the equation by 6\left(x-6\right)\left(x+6\right), the least common multiple of 6^{2}-x^{2},6x+6^{2},6x-6^{2}.

$$6\left(x-6\right)\left(x+6\right)-6\times 26-\left(x-6\right)x-\left(x+6\right)x=0$$

Use the distributive property to multiply 6 by x-6.

$$\left(6x-36\right)\left(x+6\right)-6\times 26-\left(x-6\right)x-\left(x+6\right)x=0$$

Use the distributive property to multiply 6x-36 by x+6 and combine like terms.

$$6x^{2}-216-6\times 26-\left(x-6\right)x-\left(x+6\right)x=0$$

Multiply -6 and 26 to get -156.

$$6x^{2}-216-156-\left(x-6\right)x-\left(x+6\right)x=0$$

Subtract 156 from -216 to get -372.

$$6x^{2}-372-\left(x-6\right)x-\left(x+6\right)x=0$$

Use the distributive property to multiply x-6 by x.

$$6x^{2}-372-\left(x^{2}-6x\right)-\left(x+6\right)x=0$$

To find the opposite of x^{2}-6x, find the opposite of each term.

$$6x^{2}-372-x^{2}+6x-\left(x+6\right)x=0$$

Combine 6x^{2} and -x^{2} to get 5x^{2}.

$$5x^{2}-372+6x-\left(x+6\right)x=0$$

Use the distributive property to multiply x+6 by x.

$$5x^{2}-372+6x-\left(x^{2}+6x\right)=0$$

To find the opposite of x^{2}+6x, find the opposite of each term.

$$5x^{2}-372+6x-x^{2}-6x=0$$

Combine 5x^{2} and -x^{2} to get 4x^{2}.

$$4x^{2}-372+6x-6x=0$$

Combine 6x and -6x to get 0.

$$4x^{2}-372=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and -372 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\left(-372\right)}}{2\times 4}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 4\left(-372\right)}}{2\times 4}$$

Multiply -4 times 4.

$$x=\frac{0±\sqrt{-16\left(-372\right)}}{2\times 4}$$

Multiply -16 times -372.

$$x=\frac{0±\sqrt{5952}}{2\times 4}$$

Take the square root of 5952.

$$x=\frac{0±8\sqrt{93}}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{0±8\sqrt{93}}{8}$$

Now solve the equation x=\frac{0±8\sqrt{93}}{8} when ± is plus.

$$x=\sqrt{93}$$

Now solve the equation x=\frac{0±8\sqrt{93}}{8} when ± is minus.

$$x=-\sqrt{93}$$

The equation is now solved.

$$x=\sqrt{93} x=-\sqrt{93}$$