Solve sqrt{5(x*3)}2-3x=0

$$\sqrt{ 5(x \times 3) } 2-3x = 0$$

Solve for x

$$x = \frac{20}{3} = 6\frac{2}{3} \approx 6.666666667$$

$$x=0$$

Solution Steps

Subtract -3x from both sides of the equation.

$$2\sqrt{5x\times 3}=3x$$

Multiply 5 and 3 to get 15.

$$2\sqrt{15x}=3x$$

Square both sides of the equation.

$$\left(2\sqrt{15x}\right)^{2}=\left(3x\right)^{2}$$

Expand \left(2\sqrt{15x}\right)^{2}.

$$2^{2}\left(\sqrt{15x}\right)^{2}=\left(3x\right)^{2}$$

Calculate 2 to the power of 2 and get 4.

$$4\left(\sqrt{15x}\right)^{2}=\left(3x\right)^{2}$$

Calculate \sqrt{15x} to the power of 2 and get 15x.

$$4\times 15x=\left(3x\right)^{2}$$

Multiply 4 and 15 to get 60.

$$60x=\left(3x\right)^{2}$$

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

$$60x=3^{2}x^{2}$$

Calculate 3 to the power of 2 and get 9.

$$60x=9x^{2}$$

Subtract 9x^{2} from both sides.

$$60x-9x^{2}=0$$

Factor out x.

$$x\left(60-9x\right)=0$$

To find equation solutions, solve x=0 and 60-9x=0.

$$x=0 x=\frac{20}{3}$$

Substitute 0 for x in the equation 2\sqrt{5x\times 3}-3x=0.

$$2\sqrt{5\times 0\times 3}-3\times 0=0$$

Simplify. The value x=0 satisfies the equation.

$$0=0$$

Substitute \frac{20}{3} for x in the equation 2\sqrt{5x\times 3}-3x=0.

$$2\sqrt{5\times \frac{20}{3}\times 3}-3\times \frac{20}{3}=0$$

Simplify. The value x=\frac{20}{3} satisfies the equation.

$$0=0$$

List all solutions of 2\sqrt{15x}=3x.

$$x=0 x=\frac{20}{3}$$