Solve sqrt{2h/9}+h/y=2.40

$$\sqrt { \frac { 2 h } { 9 } } + \frac { h } { y } = 2.40$$

Solve for y

$$y=-\frac{15\left(5\sqrt{2h}+36\right)h}{2\left(25h-648\right)}$$

$$h\neq \frac{648}{25}\text{ and }h>0$$

Steps for Solving Linear Equation

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by y.

$$y\sqrt{\frac{2h}{9}}+h=2.4y$$

Subtract 2.4y from both sides.

$$y\sqrt{\frac{2h}{9}}+h-2.4y=0$$

Subtract h from both sides. Anything subtracted from zero gives its negation.

$$y\sqrt{\frac{2h}{9}}-2.4y=-h$$

Combine all terms containing y.

$$\left(\sqrt{\frac{2h}{9}}-2.4\right)y=-h$$

Divide both sides by \sqrt{\frac{2}{9}h}-2.4.

$$\frac{\left(\sqrt{\frac{2h}{9}}-2.4\right)y}{\sqrt{\frac{2h}{9}}-2.4}=-\frac{h}{\sqrt{\frac{2h}{9}}-2.4}$$

Dividing by \sqrt{\frac{2}{9}h}-2.4 undoes the multiplication by \sqrt{\frac{2}{9}h}-2.4.

$$y=-\frac{h}{\sqrt{\frac{2h}{9}}-2.4}$$

Divide -h by \sqrt{\frac{2}{9}h}-2.4.

$$y=-\frac{9\left(\frac{\sqrt{2h}}{3}+2.4\right)h}{2h-51.84}$$

Variable y cannot be equal to 0.

$$y=-\frac{9\left(\frac{\sqrt{2h}}{3}+2.4\right)h}{2h-51.84}\text{, }y\neq 0$$

Solve for h

$$\left\{\begin{matrix}h=\frac{\sqrt{25+\frac{1080}{y}}y^{2}}{45}+\frac{y^{2}}{9}+\frac{12y}{5}\text{, }&y\leq -\frac{216}{5}\text{ and }\frac{\sqrt{25+\frac{1080}{y}}y^{2}}{45}+\frac{y^{2}}{9}+\frac{12y}{5}\geq 0\text{ and }y\neq 0\\h=-\frac{\sqrt{25+\frac{1080}{y}}y^{2}}{45}+\frac{y^{2}}{9}+\frac{12y}{5}\text{, }&\left(y\leq -\frac{216}{5}\text{ or }y>0\right)\text{ and }-\frac{\sqrt{25+\frac{1080}{y}}y^{2}}{45}+\frac{y^{2}}{9}+\frac{12y}{5}\geq 0\end{matrix}\right.$$