Solve 3y+5sqrt{3}x-2x=0

$$3y+5 \sqrt{ 3 } x-2x = 0$$

Solve for x

$$x=-\frac{3\left(5\sqrt{3}+2\right)y}{71}$$

Steps for Solving Linear Equation

Subtract 3y from both sides. Anything subtracted from zero gives its negation.

$$5\sqrt{3}x-2x=-3y$$

Combine all terms containing x.

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

Divide both sides by 5\sqrt{3}-2.

$$\frac{\left(5\sqrt{3}-2\right)x}{5\sqrt{3}-2}=-\frac{3y}{5\sqrt{3}-2}$$

Dividing by 5\sqrt{3}-2 undoes the multiplication by 5\sqrt{3}-2.

$$x=-\frac{3y}{5\sqrt{3}-2}$$

Divide -3y by 5\sqrt{3}-2.

$$x=-\frac{3\left(5\sqrt{3}+2\right)y}{71}$$

Solve for y

$$y=\frac{\left(2-5\sqrt{3}\right)x}{3}$$

Steps for Solving Linear Equation

Subtract 5\sqrt{3}x from both sides. Anything subtracted from zero gives its negation.

$$3y-2x=-5\sqrt{3}x$$

Add 2x to both sides.

$$3y=-5\sqrt{3}x+2x$$

Divide both sides by 3.

$$\frac{3y}{3}=\frac{\left(2-5\sqrt{3}\right)x}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$y=\frac{\left(2-5\sqrt{3}\right)x}{3}$$

Divide x\left(-5\sqrt{3}+2\right) by 3.

$$y=\frac{-5\sqrt{3}x+2x}{3}$$