Solve frac{4sqrt{6}-8}{8}=x/4sqrt{3}

$$\frac { 4 \sqrt { 6 } - 8 } { 8 } = \frac { x } { 4 \sqrt { 3 } }$$

Solve for x

$$x=2\sqrt{3}\left(\sqrt{6}-2\right)\approx 1.557078144$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 8.

$$4\sqrt{6}-8=\frac{2}{3}\times 3^{\frac{1}{2}}x$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{2}{3}\times 3^{\frac{1}{2}}x=4\sqrt{6}-8$$

Reorder the terms.

$$\frac{2}{3}\sqrt{3}x=4\sqrt{6}-8$$

The equation is in standard form.

$$\frac{2\sqrt{3}}{3}x=4\sqrt{6}-8$$

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

$$\frac{3\times \frac{2\sqrt{3}}{3}x}{2\sqrt{3}}=\frac{3\left(4\sqrt{6}-8\right)}{2\sqrt{3}}$$

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

$$x=\frac{3\left(4\sqrt{6}-8\right)}{2\sqrt{3}}$$

Divide 4\sqrt{6}-8 by \frac{2}{3}\sqrt{3}.

$$x=6\sqrt{2}-4\sqrt{3}$$