Solve y=3(5/6)^2-5(5/6)+6

$$y = 3 ( \frac { 5 } { 6 } ) ^ { 2 } - 5 ( \frac { 5 } { 6 } ) + 6$$

Solve for y

$$y = \frac{47}{12} = 3\frac{11}{12} \approx 3.916666667$$

Steps for Solving Linear Equation

Calculate \frac{5}{6} to the power of 2 and get \frac{25}{36}.

$$y=3\times \frac{25}{36}-5\times \frac{5}{6}+6$$

Express 3\times \frac{25}{36} as a single fraction.

$$y=\frac{3\times 25}{36}-5\times \frac{5}{6}+6$$

Multiply 3 and 25 to get 75.

$$y=\frac{75}{36}-5\times \frac{5}{6}+6$$

Reduce the fraction \frac{75}{36} to lowest terms by extracting and canceling out 3.

$$y=\frac{25}{12}-5\times \frac{5}{6}+6$$

Express 5\times \frac{5}{6} as a single fraction.

$$y=\frac{25}{12}-\frac{5\times 5}{6}+6$$

Multiply 5 and 5 to get 25.

$$y=\frac{25}{12}-\frac{25}{6}+6$$

Least common multiple of 12 and 6 is 12. Convert \frac{25}{12} and \frac{25}{6} to fractions with denominator 12.

$$y=\frac{25}{12}-\frac{50}{12}+6$$

Since \frac{25}{12} and \frac{50}{12} have the same denominator, subtract them by subtracting their numerators.

$$y=\frac{25-50}{12}+6$$

Subtract 50 from 25 to get -25.

$$y=-\frac{25}{12}+6$$

Convert 6 to fraction \frac{72}{12}.

$$y=-\frac{25}{12}+\frac{72}{12}$$

Since -\frac{25}{12} and \frac{72}{12} have the same denominator, add them by adding their numerators.

$$y=\frac{-25+72}{12}$$

Add -25 and 72 to get 47.

$$y=\frac{47}{12}$$

Assign y

$$y≔\frac{47}{12}$$