Solve x-6/8=4/x+6

$$\frac { x - 6 } { 8 } = \frac { 4 } { x + 6 }$$

Solve for x

$$x=2\sqrt{17}\approx 8.246211251$$

$$x=-2\sqrt{17}\approx -8.246211251$$

Steps by Finding Square Root

Variable x cannot be equal to -6 since division by zero is not defined. Multiply both sides of the equation by 8\left(x+6\right), the least common multiple of 8,x+6.

$$\left(x+6\right)\left(x-6\right)=8\times 4$$

Consider \left(x+6\right)\left(x-6\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 6.

$$x^{2}-36=8\times 4$$

Multiply 8 and 4 to get 32.

$$x^{2}-36=32$$

Add 36 to both sides.

$$x^{2}=32+36$$

Add 32 and 36 to get 68.

$$x^{2}=68$$

Take the square root of both sides of the equation.

$$x=2\sqrt{17} x=-2\sqrt{17}$$

Steps Using the Quadratic Formula

Variable x cannot be equal to -6 since division by zero is not defined. Multiply both sides of the equation by 8\left(x+6\right), the least common multiple of 8,x+6.

$$\left(x+6\right)\left(x-6\right)=8\times 4$$

Consider \left(x+6\right)\left(x-6\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 6.

$$x^{2}-36=8\times 4$$

Multiply 8 and 4 to get 32.

$$x^{2}-36=32$$

Subtract 32 from both sides.

$$x^{2}-36-32=0$$

Subtract 32 from -36 to get -68.

$$x^{2}-68=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -68 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-68\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-68\right)}}{2}$$

Multiply -4 times -68.

$$x=\frac{0±\sqrt{272}}{2}$$

Take the square root of 272.

$$x=\frac{0±4\sqrt{17}}{2}$$

Now solve the equation x=\frac{0±4\sqrt{17}}{2} when ± is plus.

$$x=2\sqrt{17}$$

Now solve the equation x=\frac{0±4\sqrt{17}}{2} when ± is minus.

$$x=-2\sqrt{17}$$

The equation is now solved.

$$x=2\sqrt{17} x=-2\sqrt{17}$$