Solve 3x^2-51/2/x^2-7x-18=0

$$\frac { 3 x ^ { 2 } - 5 \frac { 1 } { 2 } } { x ^ { 2 } - 7 x - 18 } = 0$$

Solve for x

$$x = \frac{\sqrt{66}}{6} \approx 1.354006401$$

$$x = -\frac{\sqrt{66}}{6} \approx -1.354006401$$

Steps by Finding Square Root

Variable x cannot be equal to any of the values -2,9 since division by zero is not defined. Multiply both sides of the equation by \left(x-9\right)\left(x+2\right).

$$3x^{2}-\frac{5\times 2+1}{2}=0$$

Multiply 5 and 2 to get 10.

$$3x^{2}-\frac{10+1}{2}=0$$

Add 10 and 1 to get 11.

$$3x^{2}-\frac{11}{2}=0$$

Add \frac{11}{2} to both sides. Anything plus zero gives itself.

$$3x^{2}=\frac{11}{2}$$

Divide both sides by 3.

$$x^{2}=\frac{\frac{11}{2}}{3}$$

Express \frac{\frac{11}{2}}{3} as a single fraction.

$$x^{2}=\frac{11}{2\times 3}$$

Multiply 2 and 3 to get 6.

$$x^{2}=\frac{11}{6}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{66}}{6} x=-\frac{\sqrt{66}}{6}$$

Steps Using the Quadratic Formula

Variable x cannot be equal to any of the values -2,9 since division by zero is not defined. Multiply both sides of the equation by \left(x-9\right)\left(x+2\right).

$$3x^{2}-\frac{5\times 2+1}{2}=0$$

Multiply 5 and 2 to get 10.

$$3x^{2}-\frac{10+1}{2}=0$$

Add 10 and 1 to get 11.

$$3x^{2}-\frac{11}{2}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -\frac{11}{2} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-\frac{11}{2}\right)}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-\frac{11}{2}\right)}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\left(-\frac{11}{2}\right)}}{2\times 3}$$

Multiply -12 times -\frac{11}{2}.

$$x=\frac{0±\sqrt{66}}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±\sqrt{66}}{6}$$

Now solve the equation x=\frac{0±\sqrt{66}}{6} when ± is plus.

$$x=\frac{\sqrt{66}}{6}$$

Now solve the equation x=\frac{0±\sqrt{66}}{6} when ± is minus.

$$x=-\frac{\sqrt{66}}{6}$$

The equation is now solved.

$$x=\frac{\sqrt{66}}{6} x=-\frac{\sqrt{66}}{6}$$