Solve 3/2x^2+2=3

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

Solve for x

$$x=\frac{\sqrt{6}}{3}\approx 0.816496581$$

$$x=-\frac{\sqrt{6}}{3}\approx -0.816496581$$

Steps by Finding Square Root

Subtract 2 from both sides.

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

Subtract 2 from 3 to get 1.

$$\frac{3}{2}x^{2}=1$$

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

$$x^{2}=1\times \frac{2}{3}$$

Multiply 1 and \frac{2}{3} to get \frac{2}{3}.

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

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{6}}{3} x=-\frac{\sqrt{6}}{3}$$

Steps Using the Quadratic Formula

Subtract 3 from both sides.

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

Subtract 3 from 2 to get -1.

$$\frac{3}{2}x^{2}-1=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{3}{2} for a, 0 for b, and -1 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{3}{2}\left(-1\right)}}{2\times \frac{3}{2}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{3}{2}\left(-1\right)}}{2\times \frac{3}{2}}$$

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

$$x=\frac{0±\sqrt{-6\left(-1\right)}}{2\times \frac{3}{2}}$$

Multiply -6 times -1.

$$x=\frac{0±\sqrt{6}}{2\times \frac{3}{2}}$$

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

$$x=\frac{0±\sqrt{6}}{3}$$

Now solve the equation x=\frac{0±\sqrt{6}}{3} when ± is plus.

$$x=\frac{\sqrt{6}}{3}$$

Now solve the equation x=\frac{0±\sqrt{6}}{3} when ± is minus.

$$x=-\frac{\sqrt{6}}{3}$$

The equation is now solved.

$$x=\frac{\sqrt{6}}{3} x=-\frac{\sqrt{6}}{3}$$