Solve 1/12 n^2= 7/12 n-3 5/6 n

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

n_{1} = - 39, n_{2} = 0

Evaluate

\frac{1}{12} n^{2} = \frac{7}{12} n - 3 \frac{5}{6} \times n

Simplify

More Steps

Evaluate

\frac{7}{12} n - 3 \frac{5}{6} \times n

Covert the mixed number to an improper fraction

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Convert the expressions

3 \frac{5}{6}

Multiply the denominator of the fraction by the whole number and add the numerator of the fraction

\frac{3 \times 6 + 5}{6}

Multiply the terms

\frac{18 + 5}{6}

Add the terms

\frac{23}{6}

\frac{7}{12} n - \frac{23}{6} n

Collect like terms by calculating the sum or difference of their coefficients

(\frac{7}{12} - \frac{23}{6}) n

Subtract the numbers

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Evaluate

\frac{7}{12} - \frac{23}{6}

Reduce fractions to a common denominator

\frac{7}{12} - \frac{23 \times 2}{6 \times 2}

Multiply the numbers

\frac{7}{12} - \frac{23 \times 2}{12}

Write all numerators above the common denominator

\frac{7 - 23 \times 2}{12}

Multiply the numbers

\frac{7 - 46}{12}

Subtract the numbers

\frac{- 39}{12}

Cancel out the common factor 3

\frac{- 13}{4}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

- \frac{13}{4}

- \frac{13}{4} n

\frac{1}{12} n^{2} = - \frac{13}{4} n

Move the expression to the left side

\frac{1}{12} n^{2} + \frac{13}{4} n = 0

Factor the expression

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Evaluate

\frac{1}{12} n^{2} + \frac{13}{4} n

Rewrite the expression

\frac{1}{12} n \times n + \frac{1}{12} n \times 39

Factor out \frac{1}{12} n from the expression

\frac{1}{12} n (n + 39)

\frac{1}{12} n (n + 39) = 0

When the product of factors equals 0,at least one factor is 0

\frac{1}{12} n = 0 n + 39 = 0

Solve the equation for n

n = 0 n + 39 = 0

Solve the equation for n

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Evaluate

n + 39 = 0

Move the constant to the right-hand side and change its sign

n = 0 - 39

Removing 0 doesn't change the value,so remove it from the expression

n = - 39

n = 0 n = - 39

Solution

n_{1} = - 39, n_{2} = 0

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