Solve x*3/2*x=54

$$x \times \frac{ 3 }{ 2 } \times x=54$$

Solve for x

$$x=6$$

$$x=-6$$

Steps by Finding Square Root

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

$$x^{2}\times \frac{3}{2}=54$$

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

$$x^{2}=54\times \frac{2}{3}$$

Express 54\times \frac{2}{3} as a single fraction.

$$x^{2}=\frac{54\times 2}{3}$$

Multiply 54 and 2 to get 108.

$$x^{2}=\frac{108}{3}$$

Divide 108 by 3 to get 36.

$$x^{2}=36$$

Take the square root of both sides of the equation.

$$x=6 x=-6$$

Steps Using the Quadratic Formula

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

$$x^{2}\times \frac{3}{2}=54$$

Subtract 54 from both sides.

$$x^{2}\times \frac{3}{2}-54=0$$

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.

$$\frac{3}{2}x^{2}-54=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{3}{2} for a, 0 for b, and -54 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{3}{2}\left(-54\right)}}{2\times \frac{3}{2}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{3}{2}\left(-54\right)}}{2\times \frac{3}{2}}$$

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

$$x=\frac{0±\sqrt{-6\left(-54\right)}}{2\times \frac{3}{2}}$$

Multiply -6 times -54.

$$x=\frac{0±\sqrt{324}}{2\times \frac{3}{2}}$$

Take the square root of 324.

$$x=\frac{0±18}{2\times \frac{3}{2}}$$

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

$$x=\frac{0±18}{3}$$

Now solve the equation x=\frac{0±18}{3} when ± is plus. Divide 18 by 3.

$$x=6$$

Now solve the equation x=\frac{0±18}{3} when ± is minus. Divide -18 by 3.

$$x=-6$$

The equation is now solved.

$$x=6 x=-6$$