Solve 2x-3(2+sqrt{5})=3x-7sqrt{5}

$$2 x - 3 ( 2 + \sqrt { 5 } ) = 3 x - 7 \sqrt { 5 }$$

Solve for x

$$x=4\sqrt{5}-6\approx 2.94427191$$

Steps for Solving Linear Equation

Subtract 3x from both sides.

$$2x-3\left(2+\sqrt{5}\right)-3x=-7\sqrt{5}$$

Use the distributive property to multiply -3 by 2+\sqrt{5}.

$$2x-6-3\sqrt{5}-3x=-7\sqrt{5}$$

Combine 2x and -3x to get -x.

$$-x-6-3\sqrt{5}=-7\sqrt{5}$$

Add 6 to both sides.

$$-x-3\sqrt{5}=-7\sqrt{5}+6$$

Add 3\sqrt{5} to both sides.

$$-x=-7\sqrt{5}+6+3\sqrt{5}$$

Combine -7\sqrt{5} and 3\sqrt{5} to get -4\sqrt{5}.

$$-x=-4\sqrt{5}+6$$

The equation is in standard form.

$$-x=6-4\sqrt{5}$$

Divide both sides by -1.

$$\frac{-x}{-1}=\frac{6-4\sqrt{5}}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$x=\frac{6-4\sqrt{5}}{-1}$$

Divide -4\sqrt{5}+6 by -1.

$$x=4\sqrt{5}-6$$