Solve 120x*-6x=6

$$120x \times -6x=6$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{30}i}{60}\approx -0-0.091287093i$$

$$x=\frac{\sqrt{30}i}{60}\approx 0.091287093i$$

Steps by Finding Square Root

Multiply x and x to get x^{2}.

$$120x^{2}\left(-6\right)=6$$

Multiply 120 and -6 to get -720.

$$-720x^{2}=6$$

Divide both sides by -720.

$$x^{2}=\frac{6}{-720}$$

Reduce the fraction \frac{6}{-720} to lowest terms by extracting and canceling out 6.

$$x^{2}=-\frac{1}{120}$$

The equation is now solved.

$$x=\frac{\sqrt{30}i}{60} x=-\frac{\sqrt{30}i}{60}$$

Steps Using the Quadratic Formula

Multiply x and x to get x^{2}.

$$120x^{2}\left(-6\right)=6$$

Multiply 120 and -6 to get -720.

$$-720x^{2}=6$$

Subtract 6 from both sides.

$$-720x^{2}-6=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -720 for a, 0 for b, and -6 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-720\right)\left(-6\right)}}{2\left(-720\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-720\right)\left(-6\right)}}{2\left(-720\right)}$$

Multiply -4 times -720.

$$x=\frac{0±\sqrt{2880\left(-6\right)}}{2\left(-720\right)}$$

Multiply 2880 times -6.

$$x=\frac{0±\sqrt{-17280}}{2\left(-720\right)}$$

Take the square root of -17280.

$$x=\frac{0±24\sqrt{30}i}{2\left(-720\right)}$$

Multiply 2 times -720.

$$x=\frac{0±24\sqrt{30}i}{-1440}$$

Now solve the equation x=\frac{0±24\sqrt{30}i}{-1440} when ± is plus.

$$x=-\frac{\sqrt{30}i}{60}$$

Now solve the equation x=\frac{0±24\sqrt{30}i}{-1440} when ± is minus.

$$x=\frac{\sqrt{30}i}{60}$$

The equation is now solved.

$$x=-\frac{\sqrt{30}i}{60} x=\frac{\sqrt{30}i}{60}$$