Solve 3x^2/5y=78/z

$$\frac { 3 x ^ { 2 } } { 5 y } = \frac { 78 } { z }$$

Solve for y

$$y=\frac{zx^{2}}{130}$$

$$z\neq 0\text{ and }x\neq 0$$

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 5yz, the least common multiple of 5y,z.

$$z\times 3x^{2}=5y\times 78$$

Multiply 5 and 78 to get 390.

$$z\times 3x^{2}=390y$$

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

$$390y=z\times 3x^{2}$$

The equation is in standard form.

$$390y=3zx^{2}$$

Divide both sides by 390.

$$\frac{390y}{390}=\frac{3zx^{2}}{390}$$

Dividing by 390 undoes the multiplication by 390.

$$y=\frac{3zx^{2}}{390}$$

Divide 3zx^{2} by 390.

$$y=\frac{zx^{2}}{130}$$

Variable y cannot be equal to 0.

$$y=\frac{zx^{2}}{130}\text{, }y\neq 0$$

Solve for x

$$x=\sqrt{\frac{130y}{z}}$$

$$x=-\sqrt{\frac{130y}{z}}\text{, }\left(z<0\text{ and }y<0\right)\text{ or }\left(z>0\text{ and }y>0\right)$$