Solve 2/(x^2-9)=3

$$\frac { 2 } { ( x ^ { 2 } - 9 ) } = 3$$

Solve for x

$$x = \frac{\sqrt{87}}{3} \approx 3.109126351$$

$$x = -\frac{\sqrt{87}}{3} \approx -3.109126351$$

Steps by Finding Square Root

Variable x cannot be equal to any of the values -3,3 since division by zero is not defined. Multiply both sides of the equation by \left(x-3\right)\left(x+3\right).

$$2=3\left(x-3\right)\left(x+3\right)$$

Use the distributive property to multiply 3 by x-3.

$$2=\left(3x-9\right)\left(x+3\right)$$

Use the distributive property to multiply 3x-9 by x+3 and combine like terms.

$$2=3x^{2}-27$$

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

$$3x^{2}-27=2$$

Add 27 to both sides.

$$3x^{2}=2+27$$

Add 2 and 27 to get 29.

$$3x^{2}=29$$

Divide both sides by 3.

$$x^{2}=\frac{29}{3}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{87}}{3} x=-\frac{\sqrt{87}}{3}$$

Steps Using the Quadratic Formula

Variable x cannot be equal to any of the values -3,3 since division by zero is not defined. Multiply both sides of the equation by \left(x-3\right)\left(x+3\right).

$$2=3\left(x-3\right)\left(x+3\right)$$

Use the distributive property to multiply 3 by x-3.

$$2=\left(3x-9\right)\left(x+3\right)$$

Use the distributive property to multiply 3x-9 by x+3 and combine like terms.

$$2=3x^{2}-27$$

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

$$3x^{2}-27=2$$

Subtract 2 from both sides.

$$3x^{2}-27-2=0$$

Subtract 2 from -27 to get -29.

$$3x^{2}-29=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -29 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-29\right)}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-29\right)}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\left(-29\right)}}{2\times 3}$$

Multiply -12 times -29.

$$x=\frac{0±\sqrt{348}}{2\times 3}$$

Take the square root of 348.

$$x=\frac{0±2\sqrt{87}}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±2\sqrt{87}}{6}$$

Now solve the equation x=\frac{0±2\sqrt{87}}{6} when ± is plus.

$$x=\frac{\sqrt{87}}{3}$$

Now solve the equation x=\frac{0±2\sqrt{87}}{6} when ± is minus.

$$x=-\frac{\sqrt{87}}{3}$$

The equation is now solved.

$$x=\frac{\sqrt{87}}{3} x=-\frac{\sqrt{87}}{3}$$