Solve 3x=5sqrt{x}

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

Solve for x

$$x=0$$

$$x = \frac{25}{9} = 2\frac{7}{9} \approx 2.777777778$$

Solution Steps

Square both sides of the equation.

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

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

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

Calculate 3 to the power of 2 and get 9.

$$9x^{2}=\left(5\sqrt{x}\right)^{2}$$

Expand \left(5\sqrt{x}\right)^{2}.

$$9x^{2}=5^{2}\left(\sqrt{x}\right)^{2}$$

Calculate 5 to the power of 2 and get 25.

$$9x^{2}=25\left(\sqrt{x}\right)^{2}$$

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

$$9x^{2}=25x$$

Subtract 25x from both sides.

$$9x^{2}-25x=0$$

Factor out x.

$$x\left(9x-25\right)=0$$

To find equation solutions, solve x=0 and 9x-25=0.

$$x=0 x=\frac{25}{9}$$

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

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

Simplify. The value x=0 satisfies the equation.

$$0=0$$

Substitute \frac{25}{9} for x in the equation 3x=5\sqrt{x}.

$$3\times \frac{25}{9}=5\sqrt{\frac{25}{9}}$$

Simplify. The value x=\frac{25}{9} satisfies the equation.

$$\frac{25}{3}=\frac{25}{3}$$

List all solutions of 3x=5\sqrt{x}.

$$x=0 x=\frac{25}{9}$$