Solve 18n^2-24n-90=0

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

n_{1} = - \frac{5}{3}, n_{2} = 3

Alternative Form

n_{1} = - 1. \dot{6}, n_{2} = 3

Evaluate

18 n^{2} - 24 n - 90 = 0

Factor the expression

More Steps

Evaluate

18 n^{2} - 24 n - 90

Rewrite the expression

6 \times 3 n^{2} - 6 \times 4 n - 6 \times 15

Factor out 6 from the expression

6 (3 n^{2} - 4 n - 15)

Factor the expression

More Steps

Evaluate

3 n^{2} - 4 n - 15

Rewrite the expression

3 n^{2} + (5 - 9) n - 15

Calculate

3 n^{2} + 5 n - 9 n - 15

Rewrite the expression

n \times 3 n + n \times 5 - 3 \times 3 n - 3 \times 5

Factor out n from the expression

n (3 n + 5) - 3 \times 3 n - 3 \times 5

Factor out - 3 from the expression

n (3 n + 5) - 3 (3 n + 5)

Factor out 3 n + 5 from the expression

(n - 3) (3 n + 5)

6 (n - 3) (3 n + 5)

6 (n - 3) (3 n + 5) = 0

Divide the terms

(n - 3) (3 n + 5) = 0

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

n - 3 = 0 3 n + 5 = 0

Solve the equation for n

More Steps

Evaluate

n - 3 = 0

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

n = 0 + 3

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

n = 3

n = 3 3 n + 5 = 0

Solve the equation for n

More Steps

Evaluate

3 n + 5 = 0

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

3 n = 0 - 5

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

3 n = - 5

Divide both sides

\frac{3 n}{3} = \frac{- 5}{3}

Divide the numbers

n = \frac{- 5}{3}

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

n = - \frac{5}{3}

n = 3 n = - \frac{5}{3}

Solution

n_{1} = - \frac{5}{3}, n_{2} = 3

Alternative Form

n_{1} = - 1. \dot{6}, n_{2} = 3

Show Solution