Solve 2*pi*x3/4x=24pi

$$2 \times \pi \times x \frac{ 3 }{ 4 } x=24 \pi$$

Solve for x

$$x=4$$

$$x=-4$$

Steps by Finding Square Root

Cancel out \pi on both sides.

$$2x\times \frac{3}{4}x=24$$

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

$$2x^{2}\times \frac{3}{4}=24$$

Express 2\times \frac{3}{4} as a single fraction.

$$\frac{2\times 3}{4}x^{2}=24$$

Multiply 2 and 3 to get 6.

$$\frac{6}{4}x^{2}=24$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$\frac{3}{2}x^{2}=24$$

Multiply both sides by \frac{2}{3}, the reciprocal of \frac{3}{2}.

$$x^{2}=24\times \frac{2}{3}$$

Express 24\times \frac{2}{3} as a single fraction.

$$x^{2}=\frac{24\times 2}{3}$$

Multiply 24 and 2 to get 48.

$$x^{2}=\frac{48}{3}$$

Divide 48 by 3 to get 16.

$$x^{2}=16$$

Take the square root of both sides of the equation.

$$x=4 x=-4$$

Steps Using the Quadratic Formula

Cancel out \pi on both sides.

$$2x\times \frac{3}{4}x=24$$

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

$$2x^{2}\times \frac{3}{4}=24$$

Express 2\times \frac{3}{4} as a single fraction.

$$\frac{2\times 3}{4}x^{2}=24$$

Multiply 2 and 3 to get 6.

$$\frac{6}{4}x^{2}=24$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$\frac{3}{2}x^{2}=24$$

Subtract 24 from both sides.

$$\frac{3}{2}x^{2}-24=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{3}{2} for a, 0 for b, and -24 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{3}{2}\left(-24\right)}}{2\times \frac{3}{2}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{3}{2}\left(-24\right)}}{2\times \frac{3}{2}}$$

Multiply -4 times \frac{3}{2}.

$$x=\frac{0±\sqrt{-6\left(-24\right)}}{2\times \frac{3}{2}}$$

Multiply -6 times -24.

$$x=\frac{0±\sqrt{144}}{2\times \frac{3}{2}}$$

Take the square root of 144.

$$x=\frac{0±12}{2\times \frac{3}{2}}$$

Multiply 2 times \frac{3}{2}.

$$x=\frac{0±12}{3}$$

Now solve the equation x=\frac{0±12}{3} when ± is plus. Divide 12 by 3.

$$x=4$$

Now solve the equation x=\frac{0±12}{3} when ± is minus. Divide -12 by 3.

$$x=-4$$

The equation is now solved.

$$x=4 x=-4$$