Solve 2-(1+2sqrt{3})*x+sqrt{3}+3=0

$$2 - ( 1 + 2 \sqrt { 3 } ) \cdot x + \sqrt { 3 } + 3 = 0$$

Solve for x

$$x = \frac{9 \sqrt{3} + 1}{11} \approx 1.50804157$$

Steps for Solving Linear Equation

Use the distributive property to multiply 1+2\sqrt{3} by x.

$$2-\left(x+2\sqrt{3}x\right)+\sqrt{3}+3=0$$

To find the opposite of x+2\sqrt{3}x, find the opposite of each term.

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

Add 2 and 3 to get 5.

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

Subtract 5 from both sides. Anything subtracted from zero gives its negation.

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

Subtract \sqrt{3} from both sides.

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

Combine all terms containing x.

$$\left(-1-2\sqrt{3}\right)x=-5-\sqrt{3}$$

The equation is in standard form.

$$\left(-2\sqrt{3}-1\right)x=-\sqrt{3}-5$$

Divide both sides by -1-2\sqrt{3}.

$$\frac{\left(-2\sqrt{3}-1\right)x}{-2\sqrt{3}-1}=\frac{-\sqrt{3}-5}{-2\sqrt{3}-1}$$

Dividing by -1-2\sqrt{3} undoes the multiplication by -1-2\sqrt{3}.

$$x=\frac{-\sqrt{3}-5}{-2\sqrt{3}-1}$$

Divide -5-\sqrt{3} by -1-2\sqrt{3}.

$$x=\frac{9\sqrt{3}+1}{11}$$