Solve (7/8*1/14+3/2):x=x:(9/4+frac{1}{3}*frac{3}{5}*frac{1}{5}-frac{9}{5})

$$( \frac { 7 } { 8 } \cdot \frac { 1 } { 14 } + \frac { 3 } { 2 } ) : x = x : ( \frac { 9 } { 4 } + \frac { 1 } { 3 } \cdot \frac { 3 } { 5 } \cdot \frac { 1 } { 5 } - \frac { 9 } { 5 } )$$

Solve for x

$$x=\frac{7}{8}=0.875$$

$$x=-\frac{7}{8}=-0.875$$

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.

$$\frac{7}{8}\times \frac{1}{14}+\frac{3}{2}=\frac{100}{49}xx$$

Multiply \frac{7}{8} times \frac{1}{14} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 1}{8\times 14}+\frac{3}{2}=\frac{100}{49}xx$$

Do the multiplications in the fraction \frac{7\times 1}{8\times 14}.

$$\frac{7}{112}+\frac{3}{2}=\frac{100}{49}xx$$

Reduce the fraction \frac{7}{112} to lowest terms by extracting and canceling out 7.

$$\frac{1}{16}+\frac{3}{2}=\frac{100}{49}xx$$

Least common multiple of 16 and 2 is 16. Convert \frac{1}{16} and \frac{3}{2} to fractions with denominator 16.

$$\frac{1}{16}+\frac{24}{16}=\frac{100}{49}xx$$

Since \frac{1}{16} and \frac{24}{16} have the same denominator, add them by adding their numerators.

$$\frac{1+24}{16}=\frac{100}{49}xx$$

Add 1 and 24 to get 25.

$$\frac{25}{16}=\frac{100}{49}xx$$

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

$$\frac{25}{16}=\frac{100}{49}x^{2}$$

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

$$\frac{100}{49}x^{2}=\frac{25}{16}$$

Multiply both sides by \frac{49}{100}, the reciprocal of \frac{100}{49}.

$$x^{2}=\frac{25}{16}\times \frac{49}{100}$$

Multiply \frac{25}{16} times \frac{49}{100} by multiplying numerator times numerator and denominator times denominator.

$$x^{2}=\frac{25\times 49}{16\times 100}$$

Do the multiplications in the fraction \frac{25\times 49}{16\times 100}.

$$x^{2}=\frac{1225}{1600}$$

Reduce the fraction \frac{1225}{1600} to lowest terms by extracting and canceling out 25.

$$x^{2}=\frac{49}{64}$$

Take the square root of both sides of the equation.

$$x=\frac{7}{8} x=-\frac{7}{8}$$

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.

$$\frac{7}{8}\times \frac{1}{14}+\frac{3}{2}=\frac{100}{49}xx$$

Multiply \frac{7}{8} times \frac{1}{14} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 1}{8\times 14}+\frac{3}{2}=\frac{100}{49}xx$$

Do the multiplications in the fraction \frac{7\times 1}{8\times 14}.

$$\frac{7}{112}+\frac{3}{2}=\frac{100}{49}xx$$

Reduce the fraction \frac{7}{112} to lowest terms by extracting and canceling out 7.

$$\frac{1}{16}+\frac{3}{2}=\frac{100}{49}xx$$

Least common multiple of 16 and 2 is 16. Convert \frac{1}{16} and \frac{3}{2} to fractions with denominator 16.

$$\frac{1}{16}+\frac{24}{16}=\frac{100}{49}xx$$

Since \frac{1}{16} and \frac{24}{16} have the same denominator, add them by adding their numerators.

$$\frac{1+24}{16}=\frac{100}{49}xx$$

Add 1 and 24 to get 25.

$$\frac{25}{16}=\frac{100}{49}xx$$

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

$$\frac{25}{16}=\frac{100}{49}x^{2}$$

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

$$\frac{100}{49}x^{2}=\frac{25}{16}$$

Subtract \frac{25}{16} from both sides.

$$\frac{100}{49}x^{2}-\frac{25}{16}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{100}{49} for a, 0 for b, and -\frac{25}{16} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{100}{49}\left(-\frac{25}{16}\right)}}{2\times \frac{100}{49}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{100}{49}\left(-\frac{25}{16}\right)}}{2\times \frac{100}{49}}$$

Multiply -4 times \frac{100}{49}.

$$x=\frac{0±\sqrt{-\frac{400}{49}\left(-\frac{25}{16}\right)}}{2\times \frac{100}{49}}$$

Multiply -\frac{400}{49} times -\frac{25}{16} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$x=\frac{0±\sqrt{\frac{625}{49}}}{2\times \frac{100}{49}}$$

Take the square root of \frac{625}{49}.

$$x=\frac{0±\frac{25}{7}}{2\times \frac{100}{49}}$$

Multiply 2 times \frac{100}{49}.

$$x=\frac{0±\frac{25}{7}}{\frac{200}{49}}$$

Now solve the equation x=\frac{0±\frac{25}{7}}{\frac{200}{49}} when ± is plus.

$$x=\frac{7}{8}$$

Now solve the equation x=\frac{0±\frac{25}{7}}{\frac{200}{49}} when ± is minus.

$$x=-\frac{7}{8}$$

The equation is now solved.

$$x=\frac{7}{8} x=-\frac{7}{8}$$