Solve 2.4sqrt{h}=h

$$2.4 \sqrt { h } = h$$

Solve for h

$$h=0$$

$$h=5.76$$

Solution Steps

Square both sides of the equation.

$$\left(2.4\sqrt{h}\right)^{2}=h^{2}$$

Expand \left(2.4\sqrt{h}\right)^{2}.

$$2.4^{2}\left(\sqrt{h}\right)^{2}=h^{2}$$

Calculate 2.4 to the power of 2 and get \frac{144}{25}.

$$\frac{144}{25}\left(\sqrt{h}\right)^{2}=h^{2}$$

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

$$\frac{144}{25}h=h^{2}$$

Subtract h^{2} from both sides.

$$\frac{144}{25}h-h^{2}=0$$

Factor out h.

$$h\left(\frac{144}{25}-h\right)=0$$

To find equation solutions, solve h=0 and \frac{144}{25}-h=0.

$$h=0 h=\frac{144}{25}$$

Substitute 0 for h in the equation 2.4\sqrt{h}=h.

$$2.4\sqrt{0}=0$$

Simplify. The value h=0 satisfies the equation.

$$0=0$$

Substitute \frac{144}{25} for h in the equation 2.4\sqrt{h}=h.

$$2.4\sqrt{\frac{144}{25}}=\frac{144}{25}$$

Simplify. The value h=\frac{144}{25} satisfies the equation.

$$\frac{144}{25}=\frac{144}{25}$$

List all solutions of \frac{12\sqrt{h}}{5}=h.

$$h=0 h=\frac{144}{25}$$