Solve x(3/2x)/2=24

$$\frac { x ( \frac { 3 } { 2 } x ) } { 2 } = 24$$

Solve for x

$$x=4\sqrt{2}\approx 5.656854249$$

$$x=-4\sqrt{2}\approx -5.656854249$$

Steps by Finding Square Root

Multiply both sides by 2.

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

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

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

Multiply 24 and 2 to get 48.

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

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

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

Express 48\times \frac{2}{3} as a single fraction.

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

Multiply 48 and 2 to get 96.

$$x^{2}=\frac{96}{3}$$

Divide 96 by 3 to get 32.

$$x^{2}=32$$

Take the square root of both sides of the equation.

$$x=4\sqrt{2} x=-4\sqrt{2}$$

Steps Using the Quadratic Formula

Multiply both sides by 2.

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

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

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

Multiply 24 and 2 to get 48.

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

Subtract 48 from both sides.

$$x^{2}\times \frac{3}{2}-48=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$\frac{3}{2}x^{2}-48=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{3}{2} for a, 0 for b, and -48 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{3}{2}\left(-48\right)}}{2\times \frac{3}{2}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{3}{2}\left(-48\right)}}{2\times \frac{3}{2}}$$

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

$$x=\frac{0±\sqrt{-6\left(-48\right)}}{2\times \frac{3}{2}}$$

Multiply -6 times -48.

$$x=\frac{0±\sqrt{288}}{2\times \frac{3}{2}}$$

Take the square root of 288.

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

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

$$x=\frac{0±12\sqrt{2}}{3}$$

Now solve the equation x=\frac{0±12\sqrt{2}}{3} when ± is plus.

$$x=4\sqrt{2}$$

Now solve the equation x=\frac{0±12\sqrt{2}}{3} when ± is minus.

$$x=-4\sqrt{2}$$

The equation is now solved.

$$x=4\sqrt{2} x=-4\sqrt{2}$$