Solve 120x*1.5x=240

$$120x \cdot 1.5x = 240$$

Solve for x

$$x = \frac{2 \sqrt{3}}{3} \approx 1.154700538$$

$$x = -\frac{2 \sqrt{3}}{3} \approx -1.154700538$$

Steps by Finding Square Root

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

$$120x^{2}\times 1.5=240$$

Multiply 120 and 1.5 to get 180.

$$180x^{2}=240$$

Divide both sides by 180.

$$x^{2}=\frac{240}{180}$$

Reduce the fraction \frac{240}{180} to lowest terms by extracting and canceling out 60.

$$x^{2}=\frac{4}{3}$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

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

$$120x^{2}\times 1.5=240$$

Multiply 120 and 1.5 to get 180.

$$180x^{2}=240$$

Subtract 240 from both sides.

$$180x^{2}-240=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 180 for a, 0 for b, and -240 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 180\left(-240\right)}}{2\times 180}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 180\left(-240\right)}}{2\times 180}$$

Multiply -4 times 180.

$$x=\frac{0±\sqrt{-720\left(-240\right)}}{2\times 180}$$

Multiply -720 times -240.

$$x=\frac{0±\sqrt{172800}}{2\times 180}$$

Take the square root of 172800.

$$x=\frac{0±240\sqrt{3}}{2\times 180}$$

Multiply 2 times 180.

$$x=\frac{0±240\sqrt{3}}{360}$$

Now solve the equation x=\frac{0±240\sqrt{3}}{360} when ± is plus.

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

Now solve the equation x=\frac{0±240\sqrt{3}}{360} when ± is minus.

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

The equation is now solved.

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