Solve 5n^2=24-14n

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

n_{1} = - 4, n_{2} = \frac{6}{5}

Alternative Form

n_{1} = - 4, n_{2} = 1.2

Evaluate

5 n^{2} = 24 - 14 n

Move the expression to the left side

5 n^{2} - 24 + 14 n = 0

Factor the expression

More Steps

Evaluate

5 n^{2} - 24 + 14 n

Reorder the terms

5 n^{2} + 14 n - 24

Rewrite the expression

5 n^{2} + (- 6 + 20) n - 24

Calculate

5 n^{2} - 6 n + 20 n - 24

Rewrite the expression

n \times 5 n - n \times 6 + 4 \times 5 n - 4 \times 6

Factor out n from the expression

n (5 n - 6) + 4 \times 5 n - 4 \times 6

Factor out 4 from the expression

n (5 n - 6) + 4 (5 n - 6)

Factor out 5 n - 6 from the expression

(n + 4) (5 n - 6)

(n + 4) (5 n - 6) = 0

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

5 n - 6 = 0 n + 4 = 0

Solve the equation for n

More Steps

Evaluate

5 n - 6 = 0

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

5 n = 0 + 6

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

5 n = 6

Divide both sides

\frac{5 n}{5} = \frac{6}{5}

Divide the numbers

n = \frac{6}{5}

n = \frac{6}{5} n + 4 = 0

Solve the equation for n

More Steps

Evaluate

n + 4 = 0

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

n = 0 - 4

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

n = - 4

n = \frac{6}{5} n = - 4

Solution

n_{1} = - 4, n_{2} = \frac{6}{5}

Alternative Form

n_{1} = - 4, n_{2} = 1.2

Show Solution