Solve 2x^2+9/x^2-6x=0

$$\frac{ 2 { x }^{ 2 } +9 }{ { x }^{ 2 } -6x } =0$$

Solve for x (complex solution)

$$x=-\frac{3\sqrt{2}i}{2}\approx -0-2.121320344i$$

$$x=\frac{3\sqrt{2}i}{2}\approx 2.121320344i$$

Steps by Finding Square Root

Variable x cannot be equal to any of the values 0,6 since division by zero is not defined. Multiply both sides of the equation by x\left(x-6\right).

$$2x^{2}+9=0$$

Subtract 9 from both sides. Anything subtracted from zero gives its negation.

$$2x^{2}=-9$$

Divide both sides by 2.

$$x^{2}=-\frac{9}{2}$$

The equation is now solved.

$$x=\frac{3\sqrt{2}i}{2} x=-\frac{3\sqrt{2}i}{2}$$

Steps Using the Quadratic Formula

Variable x cannot be equal to any of the values 0,6 since division by zero is not defined. Multiply both sides of the equation by x\left(x-6\right).

$$2x^{2}+9=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and 9 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\times 9}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\times 9}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\times 9}}{2\times 2}$$

Multiply -8 times 9.

$$x=\frac{0±\sqrt{-72}}{2\times 2}$$

Take the square root of -72.

$$x=\frac{0±6\sqrt{2}i}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±6\sqrt{2}i}{4}$$

Now solve the equation x=\frac{0±6\sqrt{2}i}{4} when ± is plus.

$$x=\frac{3\sqrt{2}i}{2}$$

Now solve the equation x=\frac{0±6\sqrt{2}i}{4} when ± is minus.

$$x=-\frac{3\sqrt{2}i}{2}$$

The equation is now solved.

$$x=\frac{3\sqrt{2}i}{2} x=-\frac{3\sqrt{2}i}{2}$$