Solve 3n^2-n=234 - ScanMath

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

n_{1} = - \frac{26}{3}, n_{2} = 9

Alternative Form

n_{1} = - 8. \dot{6}, n_{2} = 9

Evaluate

3 n^{2} - n = 234

Move the expression to the left side

3 n^{2} - n - 234 = 0

Factor the expression

More Steps

Evaluate

3 n^{2} - n - 234

Rewrite the expression

3 n^{2} + (26 - 27) n - 234

Calculate

3 n^{2} + 26 n - 27 n - 234

Rewrite the expression

n \times 3 n + n \times 26 - 9 \times 3 n - 9 \times 26

Factor out n from the expression

n (3 n + 26) - 9 \times 3 n - 9 \times 26

Factor out - 9 from the expression

n (3 n + 26) - 9 (3 n + 26)

Factor out 3 n + 26 from the expression

(n - 9) (3 n + 26)

(n - 9) (3 n + 26) = 0

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

n - 9 = 0 3 n + 26 = 0

Solve the equation for n

More Steps

Evaluate

n - 9 = 0

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

n = 0 + 9

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

n = 9

n = 9 3 n + 26 = 0

Solve the equation for n

More Steps

Evaluate

3 n + 26 = 0

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

3 n = 0 - 26

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

3 n = - 26

Divide both sides

\frac{3 n}{3} = \frac{- 26}{3}

Divide the numbers

n = \frac{- 26}{3}

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

n = - \frac{26}{3}

n = 9 n = - \frac{26}{3}

Solution

n_{1} = - \frac{26}{3}, n_{2} = 9

Alternative Form

n_{1} = - 8. \dot{6}, n_{2} = 9

Show Solution