Solve (7x+12y/25*sqrt{47})div4x=2

$$( \frac{ 7x+12y }{ 25 } \times \sqrt{ 47 } ) \div 4x=2$$

Solve for y

$$y=-\frac{7x}{12}+\frac{50\sqrt{47}}{141x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4.

$$\frac{7x+12y}{25}\sqrt{47}x=8$$

Express \frac{7x+12y}{25}\sqrt{47} as a single fraction.

$$\frac{\left(7x+12y\right)\sqrt{47}}{25}x=8$$

Express \frac{\left(7x+12y\right)\sqrt{47}}{25}x as a single fraction.

$$\frac{\left(7x+12y\right)\sqrt{47}x}{25}=8$$

Use the distributive property to multiply 7x+12y by \sqrt{47}.

$$\frac{\left(7x\sqrt{47}+12y\sqrt{47}\right)x}{25}=8$$

Use the distributive property to multiply 7x\sqrt{47}+12y\sqrt{47} by x.

$$\frac{7\sqrt{47}x^{2}+12y\sqrt{47}x}{25}=8$$

Multiply both sides by 25.

$$7\sqrt{47}x^{2}+12y\sqrt{47}x=8\times 25$$

Multiply 8 and 25 to get 200.

$$7\sqrt{47}x^{2}+12y\sqrt{47}x=200$$

Subtract 7\sqrt{47}x^{2} from both sides.

$$12y\sqrt{47}x=200-7\sqrt{47}x^{2}$$

The equation is in standard form.

$$12\sqrt{47}xy=-7\sqrt{47}x^{2}+200$$

Divide both sides by 12\sqrt{47}x.

$$\frac{12\sqrt{47}xy}{12\sqrt{47}x}=\frac{-7\sqrt{47}x^{2}+200}{12\sqrt{47}x}$$

Dividing by 12\sqrt{47}x undoes the multiplication by 12\sqrt{47}x.

$$y=\frac{-7\sqrt{47}x^{2}+200}{12\sqrt{47}x}$$

Divide 200-7\sqrt{47}x^{2} by 12\sqrt{47}x.

$$y=-\frac{7x}{12}+\frac{50\sqrt{47}}{141x}$$

Solve for x

$$x=\frac{2\sqrt{19881y^{2}+16450\sqrt{47}}}{329}-\frac{6y}{7}$$

$$x=-\frac{2\sqrt{19881y^{2}+16450\sqrt{47}}}{329}-\frac{6y}{7}$$