Solve 4div5/2=left(3xright)^2

$$\frac{ 4 \div 5 }{ 2 } = { \left(3x \right) }^{ 2 }$$

Solve for x

$$x=\frac{\sqrt{10}}{15}\approx 0.210818511$$

$$x=-\frac{\sqrt{10}}{15}\approx -0.210818511$$

Steps by Finding Square Root

Express \frac{\frac{4}{5}}{2} as a single fraction.

$$\frac{4}{5\times 2}=\left(3x\right)^{2}$$

Multiply 5 and 2 to get 10.

$$\frac{4}{10}=\left(3x\right)^{2}$$

Reduce the fraction \frac{4}{10} to lowest terms by extracting and canceling out 2.

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

Expand \left(3x\right)^{2}.

$$\frac{2}{5}=3^{2}x^{2}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{2}{5}=9x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$9x^{2}=\frac{2}{5}$$

Divide both sides by 9.

$$x^{2}=\frac{\frac{2}{5}}{9}$$

Express \frac{\frac{2}{5}}{9} as a single fraction.

$$x^{2}=\frac{2}{5\times 9}$$

Multiply 5 and 9 to get 45.

$$x^{2}=\frac{2}{45}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{10}}{15} x=-\frac{\sqrt{10}}{15}$$

Steps Using the Quadratic Formula

Express \frac{\frac{4}{5}}{2} as a single fraction.

$$\frac{4}{5\times 2}=\left(3x\right)^{2}$$

Multiply 5 and 2 to get 10.

$$\frac{4}{10}=\left(3x\right)^{2}$$

Reduce the fraction \frac{4}{10} to lowest terms by extracting and canceling out 2.

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

Expand \left(3x\right)^{2}.

$$\frac{2}{5}=3^{2}x^{2}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{2}{5}=9x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$9x^{2}=\frac{2}{5}$$

Subtract \frac{2}{5} from both sides.

$$9x^{2}-\frac{2}{5}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 9 for a, 0 for b, and -\frac{2}{5} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 9\left(-\frac{2}{5}\right)}}{2\times 9}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 9\left(-\frac{2}{5}\right)}}{2\times 9}$$

Multiply -4 times 9.

$$x=\frac{0±\sqrt{-36\left(-\frac{2}{5}\right)}}{2\times 9}$$

Multiply -36 times -\frac{2}{5}.

$$x=\frac{0±\sqrt{\frac{72}{5}}}{2\times 9}$$

Take the square root of \frac{72}{5}.

$$x=\frac{0±\frac{6\sqrt{10}}{5}}{2\times 9}$$

Multiply 2 times 9.

$$x=\frac{0±\frac{6\sqrt{10}}{5}}{18}$$

Now solve the equation x=\frac{0±\frac{6\sqrt{10}}{5}}{18} when ± is plus.

$$x=\frac{\sqrt{10}}{15}$$

Now solve the equation x=\frac{0±\frac{6\sqrt{10}}{5}}{18} when ± is minus.

$$x=-\frac{\sqrt{10}}{15}$$

The equation is now solved.

$$x=\frac{\sqrt{10}}{15} x=-\frac{\sqrt{10}}{15}$$