Solve 5-frac{12/5sqrt{2}}{x}=4/sqrt{2/2}

$$\frac { 5 - \frac { 12 } { 5 } \sqrt { 2 } } { x } = \frac { 4 } { \frac { \sqrt { 2 } } { 2 } }$$

Solve for x

$$x=\frac{5\sqrt{2}}{8}-\frac{3}{5}\approx 0.283883476$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$5-\frac{12}{5}\sqrt{2}=x\times 2^{\frac{1}{2}}\times 4$$

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

$$x\times 2^{\frac{1}{2}}\times 4=5-\frac{12}{5}\sqrt{2}$$

Reorder the terms.

$$4\sqrt{2}x=-\frac{12}{5}\sqrt{2}+5$$

The equation is in standard form.

$$4\sqrt{2}x=-\frac{12\sqrt{2}}{5}+5$$

Divide both sides by 4\sqrt{2}.

$$\frac{4\sqrt{2}x}{4\sqrt{2}}=\frac{-\frac{12\sqrt{2}}{5}+5}{4\sqrt{2}}$$

Dividing by 4\sqrt{2} undoes the multiplication by 4\sqrt{2}.

$$x=\frac{-\frac{12\sqrt{2}}{5}+5}{4\sqrt{2}}$$

Divide 5-\frac{12\sqrt{2}}{5} by 4\sqrt{2}.

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