Solve 4a+2sqrt{3}a=3+sqrt{3}

$$4 a + 2 \sqrt { 3 } a = 3 + \sqrt { 3 }$$

Solve for a

$$a=\frac{3-\sqrt{3}}{2}\approx 0.633974596$$

Steps for Solving Linear Equation

Combine all terms containing a.

$$\left(4+2\sqrt{3}\right)a=3+\sqrt{3}$$

The equation is in standard form.

$$\left(2\sqrt{3}+4\right)a=\sqrt{3}+3$$

Divide both sides by 4+2\sqrt{3}.

$$\frac{\left(2\sqrt{3}+4\right)a}{2\sqrt{3}+4}=\frac{\sqrt{3}+3}{2\sqrt{3}+4}$$

Dividing by 4+2\sqrt{3} undoes the multiplication by 4+2\sqrt{3}.

$$a=\frac{\sqrt{3}+3}{2\sqrt{3}+4}$$

Divide 3+\sqrt{3} by 4+2\sqrt{3}.

$$a=\frac{3-\sqrt{3}}{2}$$