Solve frac{5sqrt{2}*sqrt{3}}{2}=frac{x/sqrt{2(sqrt{3}+1)}}{4}

$$\frac { 5 \sqrt { 2 } \times \sqrt { 3 } } { 2 } = \frac { \frac { x } { \sqrt { 2 } ( \sqrt { 3 } + 1 ) } } { 4 }$$

Solve for x

$$x=20\sqrt{3}+60\approx 94.641016151$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4, the least common multiple of 2,4.

$$2\times 5\sqrt{2}\sqrt{3}=\frac{x}{\sqrt{2}\left(\sqrt{3}+1\right)}$$

Multiply 2 and 5 to get 10.

$$10\sqrt{2}\sqrt{3}=\frac{x}{\sqrt{2}\left(\sqrt{3}+1\right)}$$

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

$$10\sqrt{6}=\frac{x}{\sqrt{2}\left(\sqrt{3}+1\right)}$$

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

$$\frac{x}{\sqrt{2}\left(\sqrt{3}+1\right)}=10\sqrt{6}$$

The equation is in standard form.

$$\frac{1}{\sqrt{2}\left(\sqrt{3}+1\right)}x=10\sqrt{6}$$

Divide both sides by \left(\sqrt{2}\right)^{-1}\left(\sqrt{3}+1\right)^{-1}.

$$\frac{\frac{1}{\sqrt{2}\left(\sqrt{3}+1\right)}x\sqrt{2}\left(\sqrt{3}+1\right)}{1}=\frac{10\sqrt{6}\sqrt{2}\left(\sqrt{3}+1\right)}{1}$$

Dividing by \left(\sqrt{2}\right)^{-1}\left(\sqrt{3}+1\right)^{-1} undoes the multiplication by \left(\sqrt{2}\right)^{-1}\left(\sqrt{3}+1\right)^{-1}.

$$x=\frac{10\sqrt{6}\sqrt{2}\left(\sqrt{3}+1\right)}{1}$$

Divide 10\sqrt{6} by \left(\sqrt{2}\right)^{-1}\left(\sqrt{3}+1\right)^{-1}.

$$x=20\sqrt{3}+60$$