Solve x=1.5/frac{76.2{2}*sqrt{4*59.2/76.2*(1-59.2/76.2)}}

$$x= \frac{ 1.5 }{ \frac{ 76.2 }{ 2 } \times \sqrt{ \frac{ 4 \times 59.2 }{ 76.2 } \times (1- \frac{ 59.2 }{ 76.2 } ) } }$$

Solve for x

$$x=\frac{3\sqrt{6290}}{5032}\approx 0.0472831$$

Steps for Solving Linear Equation

Expand \frac{76.2}{2} by multiplying both numerator and the denominator by 10.

$$x=\frac{1.5}{\frac{762}{20}\sqrt{\frac{4\times 59.2}{76.2}\left(1-\frac{59.2}{76.2}\right)}}$$

Reduce the fraction \frac{762}{20} to lowest terms by extracting and canceling out 2.

$$x=\frac{1.5}{\frac{381}{10}\sqrt{\frac{4\times 59.2}{76.2}\left(1-\frac{59.2}{76.2}\right)}}$$

Multiply 4 and 59.2 to get 236.8.

$$x=\frac{1.5}{\frac{381}{10}\sqrt{\frac{236.8}{76.2}\left(1-\frac{59.2}{76.2}\right)}}$$

Expand \frac{236.8}{76.2} by multiplying both numerator and the denominator by 10.

$$x=\frac{1.5}{\frac{381}{10}\sqrt{\frac{2368}{762}\left(1-\frac{59.2}{76.2}\right)}}$$

Reduce the fraction \frac{2368}{762} to lowest terms by extracting and canceling out 2.

$$x=\frac{1.5}{\frac{381}{10}\sqrt{\frac{1184}{381}\left(1-\frac{59.2}{76.2}\right)}}$$

Expand \frac{59.2}{76.2} by multiplying both numerator and the denominator by 10.

$$x=\frac{1.5}{\frac{381}{10}\sqrt{\frac{1184}{381}\left(1-\frac{592}{762}\right)}}$$

Reduce the fraction \frac{592}{762} to lowest terms by extracting and canceling out 2.

$$x=\frac{1.5}{\frac{381}{10}\sqrt{\frac{1184}{381}\left(1-\frac{296}{381}\right)}}$$

Convert 1 to fraction \frac{381}{381}.

$$x=\frac{1.5}{\frac{381}{10}\sqrt{\frac{1184}{381}\left(\frac{381}{381}-\frac{296}{381}\right)}}$$

Since \frac{381}{381} and \frac{296}{381} have the same denominator, subtract them by subtracting their numerators.

$$x=\frac{1.5}{\frac{381}{10}\sqrt{\frac{1184}{381}\times \frac{381-296}{381}}}$$

Subtract 296 from 381 to get 85.

$$x=\frac{1.5}{\frac{381}{10}\sqrt{\frac{1184}{381}\times \frac{85}{381}}}$$

Multiply \frac{1184}{381} times \frac{85}{381} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{1.5}{\frac{381}{10}\sqrt{\frac{1184\times 85}{381\times 381}}}$$

Do the multiplications in the fraction \frac{1184\times 85}{381\times 381}.

$$x=\frac{1.5}{\frac{381}{10}\sqrt{\frac{100640}{145161}}}$$

Rewrite the square root of the division \sqrt{\frac{100640}{145161}} as the division of square roots \frac{\sqrt{100640}}{\sqrt{145161}}.

$$x=\frac{1.5}{\frac{381}{10}\times \frac{\sqrt{100640}}{\sqrt{145161}}}$$

Factor 100640=4^{2}\times 6290. Rewrite the square root of the product \sqrt{4^{2}\times 6290} as the product of square roots \sqrt{4^{2}}\sqrt{6290}. Take the square root of 4^{2}.

$$x=\frac{1.5}{\frac{381}{10}\times \frac{4\sqrt{6290}}{\sqrt{145161}}}$$

Calculate the square root of 145161 and get 381.

$$x=\frac{1.5}{\frac{381}{10}\times \frac{4\sqrt{6290}}{381}}$$

Multiply \frac{381}{10} times \frac{4\sqrt{6290}}{381} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{1.5}{\frac{381\times 4\sqrt{6290}}{10\times 381}}$$

Cancel out 2\times 381 in both numerator and denominator.

$$x=\frac{1.5}{\frac{2\sqrt{6290}}{5}}$$

Divide 1.5 by \frac{2\sqrt{6290}}{5} by multiplying 1.5 by the reciprocal of \frac{2\sqrt{6290}}{5}.

$$x=\frac{1.5\times 5}{2\sqrt{6290}}$$

Rationalize the denominator of \frac{1.5\times 5}{2\sqrt{6290}} by multiplying numerator and denominator by \sqrt{6290}.

$$x=\frac{1.5\times 5\sqrt{6290}}{2\left(\sqrt{6290}\right)^{2}}$$

The square of \sqrt{6290} is 6290.

$$x=\frac{1.5\times 5\sqrt{6290}}{2\times 6290}$$

Multiply 1.5 and 5 to get 7.5.

$$x=\frac{7.5\sqrt{6290}}{2\times 6290}$$

Multiply 2 and 6290 to get 12580.

$$x=\frac{7.5\sqrt{6290}}{12580}$$

Divide 7.5\sqrt{6290} by 12580 to get \frac{3}{5032}\sqrt{6290}.

$$x=\frac{3}{5032}\sqrt{6290}$$

Assign x

$$x≔\frac{3\sqrt{6290}}{5032}$$