Solve 11/8left(3/11+1/6+frac{3/2right)}{x}=frac{x}{frac{frac{5}{3}-frac{1}{4}+frac{3}{2}}{frac{7}{6}}frac{20}{3}}

$$\frac{ \frac{ 11 }{ 8 } \left( \frac{ 3 }{ 11 } + \frac{ 1 }{ 6 } + \frac{ 3 }{ 2 } \right) }{ x } = \frac{ x }{ \frac{ \frac{ 5 }{ 3 } - \frac{ 1 }{ 4 } + \frac{ 3 }{ 2 } }{ \frac{ 7 }{ 6 } } \frac{ 20 }{ 3 } }$$

Solve for x

$$x = \frac{20}{3} = 6\frac{2}{3} \approx 6.666666667$$

$$x = -\frac{20}{3} = -6\frac{2}{3} \approx -6.666666667$$

Steps by Finding Square Root

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

$$\frac{11}{8}\left(\frac{3}{11}+\frac{1}{6}+\frac{3}{2}\right)=\frac{3}{50}xx$$

Least common multiple of 11 and 6 is 66. Convert \frac{3}{11} and \frac{1}{6} to fractions with denominator 66.

$$\frac{11}{8}\left(\frac{18}{66}+\frac{11}{66}+\frac{3}{2}\right)=\frac{3}{50}xx$$

Since \frac{18}{66} and \frac{11}{66} have the same denominator, add them by adding their numerators.

$$\frac{11}{8}\left(\frac{18+11}{66}+\frac{3}{2}\right)=\frac{3}{50}xx$$

Add 18 and 11 to get 29.

$$\frac{11}{8}\left(\frac{29}{66}+\frac{3}{2}\right)=\frac{3}{50}xx$$

Least common multiple of 66 and 2 is 66. Convert \frac{29}{66} and \frac{3}{2} to fractions with denominator 66.

$$\frac{11}{8}\left(\frac{29}{66}+\frac{99}{66}\right)=\frac{3}{50}xx$$

Since \frac{29}{66} and \frac{99}{66} have the same denominator, add them by adding their numerators.

$$\frac{11}{8}\times \frac{29+99}{66}=\frac{3}{50}xx$$

Add 29 and 99 to get 128.

$$\frac{11}{8}\times \frac{128}{66}=\frac{3}{50}xx$$

Reduce the fraction \frac{128}{66} to lowest terms by extracting and canceling out 2.

$$\frac{11}{8}\times \frac{64}{33}=\frac{3}{50}xx$$

Multiply \frac{11}{8} times \frac{64}{33} by multiplying numerator times numerator and denominator times denominator.

$$\frac{11\times 64}{8\times 33}=\frac{3}{50}xx$$

Do the multiplications in the fraction \frac{11\times 64}{8\times 33}.

$$\frac{704}{264}=\frac{3}{50}xx$$

Reduce the fraction \frac{704}{264} to lowest terms by extracting and canceling out 88.

$$\frac{8}{3}=\frac{3}{50}xx$$

Multiply x and x to get x^{2}.

$$\frac{8}{3}=\frac{3}{50}x^{2}$$

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

$$\frac{3}{50}x^{2}=\frac{8}{3}$$

Multiply both sides by \frac{50}{3}, the reciprocal of \frac{3}{50}.

$$x^{2}=\frac{8}{3}\times \frac{50}{3}$$

Multiply \frac{8}{3} times \frac{50}{3} by multiplying numerator times numerator and denominator times denominator.

$$x^{2}=\frac{8\times 50}{3\times 3}$$

Do the multiplications in the fraction \frac{8\times 50}{3\times 3}.

$$x^{2}=\frac{400}{9}$$

Take the square root of both sides of the equation.

$$x=\frac{20}{3} x=-\frac{20}{3}$$

Steps Using the Quadratic Formula

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

$$\frac{11}{8}\left(\frac{3}{11}+\frac{1}{6}+\frac{3}{2}\right)=\frac{3}{50}xx$$

Least common multiple of 11 and 6 is 66. Convert \frac{3}{11} and \frac{1}{6} to fractions with denominator 66.

$$\frac{11}{8}\left(\frac{18}{66}+\frac{11}{66}+\frac{3}{2}\right)=\frac{3}{50}xx$$

Since \frac{18}{66} and \frac{11}{66} have the same denominator, add them by adding their numerators.

$$\frac{11}{8}\left(\frac{18+11}{66}+\frac{3}{2}\right)=\frac{3}{50}xx$$

Add 18 and 11 to get 29.

$$\frac{11}{8}\left(\frac{29}{66}+\frac{3}{2}\right)=\frac{3}{50}xx$$

Least common multiple of 66 and 2 is 66. Convert \frac{29}{66} and \frac{3}{2} to fractions with denominator 66.

$$\frac{11}{8}\left(\frac{29}{66}+\frac{99}{66}\right)=\frac{3}{50}xx$$

Since \frac{29}{66} and \frac{99}{66} have the same denominator, add them by adding their numerators.

$$\frac{11}{8}\times \frac{29+99}{66}=\frac{3}{50}xx$$

Add 29 and 99 to get 128.

$$\frac{11}{8}\times \frac{128}{66}=\frac{3}{50}xx$$

Reduce the fraction \frac{128}{66} to lowest terms by extracting and canceling out 2.

$$\frac{11}{8}\times \frac{64}{33}=\frac{3}{50}xx$$

Multiply \frac{11}{8} times \frac{64}{33} by multiplying numerator times numerator and denominator times denominator.

$$\frac{11\times 64}{8\times 33}=\frac{3}{50}xx$$

Do the multiplications in the fraction \frac{11\times 64}{8\times 33}.

$$\frac{704}{264}=\frac{3}{50}xx$$

Reduce the fraction \frac{704}{264} to lowest terms by extracting and canceling out 88.

$$\frac{8}{3}=\frac{3}{50}xx$$

Multiply x and x to get x^{2}.

$$\frac{8}{3}=\frac{3}{50}x^{2}$$

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

$$\frac{3}{50}x^{2}=\frac{8}{3}$$

Subtract \frac{8}{3} from both sides.

$$\frac{3}{50}x^{2}-\frac{8}{3}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{3}{50} for a, 0 for b, and -\frac{8}{3} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{3}{50}\left(-\frac{8}{3}\right)}}{2\times \frac{3}{50}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{3}{50}\left(-\frac{8}{3}\right)}}{2\times \frac{3}{50}}$$

Multiply -4 times \frac{3}{50}.

$$x=\frac{0±\sqrt{-\frac{6}{25}\left(-\frac{8}{3}\right)}}{2\times \frac{3}{50}}$$

Multiply -\frac{6}{25} times -\frac{8}{3} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$x=\frac{0±\sqrt{\frac{16}{25}}}{2\times \frac{3}{50}}$$

Take the square root of \frac{16}{25}.

$$x=\frac{0±\frac{4}{5}}{2\times \frac{3}{50}}$$

Multiply 2 times \frac{3}{50}.

$$x=\frac{0±\frac{4}{5}}{\frac{3}{25}}$$

Now solve the equation x=\frac{0±\frac{4}{5}}{\frac{3}{25}} when ± is plus.

$$x=\frac{20}{3}$$

Now solve the equation x=\frac{0±\frac{4}{5}}{\frac{3}{25}} when ± is minus.

$$x=-\frac{20}{3}$$

The equation is now solved.

$$x=\frac{20}{3} x=-\frac{20}{3}$$