Solve (8/5+1/3):x=x:(1+14/15)

$$( \frac { 8 } { 5 } + \frac { 1 } { 3 } ) : x = x : ( 1 + \frac { 14 } { 15 } )$$

Solve for x

$$x = \frac{29}{15} = 1\frac{14}{15} \approx 1.933333333$$

$$x = -\frac{29}{15} = -1\frac{14}{15} \approx -1.933333333$$

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.

$$\frac{8}{5}+\frac{1}{3}=\frac{15}{29}xx$$

Least common multiple of 5 and 3 is 15. Convert \frac{8}{5} and \frac{1}{3} to fractions with denominator 15.

$$\frac{24}{15}+\frac{5}{15}=\frac{15}{29}xx$$

Since \frac{24}{15} and \frac{5}{15} have the same denominator, add them by adding their numerators.

$$\frac{24+5}{15}=\frac{15}{29}xx$$

Add 24 and 5 to get 29.

$$\frac{29}{15}=\frac{15}{29}xx$$

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

$$\frac{29}{15}=\frac{15}{29}x^{2}$$

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

$$\frac{15}{29}x^{2}=\frac{29}{15}$$

Multiply both sides by \frac{29}{15}, the reciprocal of \frac{15}{29}.

$$x^{2}=\frac{29}{15}\times \frac{29}{15}$$

Multiply \frac{29}{15} times \frac{29}{15} by multiplying numerator times numerator and denominator times denominator.

$$x^{2}=\frac{29\times 29}{15\times 15}$$

Do the multiplications in the fraction \frac{29\times 29}{15\times 15}.

$$x^{2}=\frac{841}{225}$$

Take the square root of both sides of the equation.

$$x=\frac{29}{15} x=-\frac{29}{15}$$

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.

$$\frac{8}{5}+\frac{1}{3}=\frac{15}{29}xx$$

Least common multiple of 5 and 3 is 15. Convert \frac{8}{5} and \frac{1}{3} to fractions with denominator 15.

$$\frac{24}{15}+\frac{5}{15}=\frac{15}{29}xx$$

Since \frac{24}{15} and \frac{5}{15} have the same denominator, add them by adding their numerators.

$$\frac{24+5}{15}=\frac{15}{29}xx$$

Add 24 and 5 to get 29.

$$\frac{29}{15}=\frac{15}{29}xx$$

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

$$\frac{29}{15}=\frac{15}{29}x^{2}$$

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

$$\frac{15}{29}x^{2}=\frac{29}{15}$$

Subtract \frac{29}{15} from both sides.

$$\frac{15}{29}x^{2}-\frac{29}{15}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{15}{29} for a, 0 for b, and -\frac{29}{15} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{15}{29}\left(-\frac{29}{15}\right)}}{2\times \frac{15}{29}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{15}{29}\left(-\frac{29}{15}\right)}}{2\times \frac{15}{29}}$$

Multiply -4 times \frac{15}{29}.

$$x=\frac{0±\sqrt{-\frac{60}{29}\left(-\frac{29}{15}\right)}}{2\times \frac{15}{29}}$$

Multiply -\frac{60}{29} times -\frac{29}{15} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$x=\frac{0±\sqrt{4}}{2\times \frac{15}{29}}$$

Take the square root of 4.

$$x=\frac{0±2}{2\times \frac{15}{29}}$$

Multiply 2 times \frac{15}{29}.

$$x=\frac{0±2}{\frac{30}{29}}$$

Now solve the equation x=\frac{0±2}{\frac{30}{29}} when ± is plus. Divide 2 by \frac{30}{29} by multiplying 2 by the reciprocal of \frac{30}{29}.

$$x=\frac{29}{15}$$

Now solve the equation x=\frac{0±2}{\frac{30}{29}} when ± is minus. Divide -2 by \frac{30}{29} by multiplying -2 by the reciprocal of \frac{30}{29}.

$$x=-\frac{29}{15}$$

The equation is now solved.

$$x=\frac{29}{15} x=-\frac{29}{15}$$