Solve 6=frac{3sqrt{2}x}{8-x}

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

Solve for x

$$x=16-8\sqrt{2}\approx 4.686291501$$

Steps for Solving Linear Equation

Variable x cannot be equal to 8 since division by zero is not defined. Multiply both sides of the equation by -x+8.

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

Use the distributive property to multiply 6 by -x+8.

$$-6x+48=3\sqrt{2}x$$

Subtract 3\sqrt{2}x from both sides.

$$-6x+48-3\sqrt{2}x=0$$

Subtract 48 from both sides. Anything subtracted from zero gives its negation.

$$-6x-3\sqrt{2}x=-48$$

Combine all terms containing x.

$$\left(-6-3\sqrt{2}\right)x=-48$$

The equation is in standard form.

$$\left(-3\sqrt{2}-6\right)x=-48$$

Divide both sides by -6-3\sqrt{2}.

$$\frac{\left(-3\sqrt{2}-6\right)x}{-3\sqrt{2}-6}=-\frac{48}{-3\sqrt{2}-6}$$

Dividing by -6-3\sqrt{2} undoes the multiplication by -6-3\sqrt{2}.

$$x=-\frac{48}{-3\sqrt{2}-6}$$

Divide -48 by -6-3\sqrt{2}.

$$x=16-8\sqrt{2}$$