Solve 2sqrt{3}x+5sqrt{2}=sqrt{48}x-sqrt{8}

$$2 \sqrt { 3 } x + 5 \sqrt { 2 } = \sqrt { 48 } x - \sqrt { 8 }$$

Solve for x

$$x = \frac{7 \sqrt{6}}{6} \approx 2.857738033$$

Steps for Solving Linear Equation

Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.

$$2\sqrt{3}x+5\sqrt{2}=4\sqrt{3}x-\sqrt{8}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$2\sqrt{3}x+5\sqrt{2}=4\sqrt{3}x-2\sqrt{2}$$

Subtract 4\sqrt{3}x from both sides.

$$2\sqrt{3}x+5\sqrt{2}-4\sqrt{3}x=-2\sqrt{2}$$

Combine 2\sqrt{3}x and -4\sqrt{3}x to get -2\sqrt{3}x.

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

Subtract 5\sqrt{2} from both sides.

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

Combine -2\sqrt{2} and -5\sqrt{2} to get -7\sqrt{2}.

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

The equation is in standard form.

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

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

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

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

$$x=-\frac{7\sqrt{2}}{-2\sqrt{3}}$$

Divide -7\sqrt{2} by -2\sqrt{3}.

$$x=\frac{7\sqrt{6}}{6}$$