Solve 3x^2=5-{left(3/2right)}^2

$$3 { x }^{ 2 } =5- { \left( \frac{ 3 }{ 2 } \right) }^{ 2 }$$

Solve for x

$$x=\frac{\sqrt{33}}{6}\approx 0.957427108$$

$$x=-\frac{\sqrt{33}}{6}\approx -0.957427108$$

Steps by Finding Square Root

Calculate \frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$3x^{2}=5-\frac{9}{4}$$

Subtract \frac{9}{4} from 5 to get \frac{11}{4}.

$$3x^{2}=\frac{11}{4}$$

Divide both sides by 3.

$$x^{2}=\frac{\frac{11}{4}}{3}$$

Express \frac{\frac{11}{4}}{3} as a single fraction.

$$x^{2}=\frac{11}{4\times 3}$$

Multiply 4 and 3 to get 12.

$$x^{2}=\frac{11}{12}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{33}}{6} x=-\frac{\sqrt{33}}{6}$$

Steps Using the Quadratic Formula

Calculate \frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$3x^{2}=5-\frac{9}{4}$$

Subtract \frac{9}{4} from 5 to get \frac{11}{4}.

$$3x^{2}=\frac{11}{4}$$

Subtract \frac{11}{4} from both sides.

$$3x^{2}-\frac{11}{4}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -\frac{11}{4} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-\frac{11}{4}\right)}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-\frac{11}{4}\right)}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\left(-\frac{11}{4}\right)}}{2\times 3}$$

Multiply -12 times -\frac{11}{4}.

$$x=\frac{0±\sqrt{33}}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±\sqrt{33}}{6}$$

Now solve the equation x=\frac{0±\sqrt{33}}{6} when ± is plus.

$$x=\frac{\sqrt{33}}{6}$$

Now solve the equation x=\frac{0±\sqrt{33}}{6} when ± is minus.

$$x=-\frac{\sqrt{33}}{6}$$

The equation is now solved.

$$x=\frac{\sqrt{33}}{6} x=-\frac{\sqrt{33}}{6}$$