Solve 3k^2 + 9k - 20 = 2k

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

k_{1} = - 4, k_{2} = \frac{5}{3}

Alternative Form

k_{1} = - 4, k_{2} = 1. \dot{6}

Evaluate

3 k^{2} + 9 k - 20 = 2 k

Move the expression to the left side

3 k^{2} + 7 k - 20 = 0

Factor the expression

More Steps

Evaluate

3 k^{2} + 7 k - 20

Rewrite the expression

3 k^{2} + (- 5 + 12) k - 20

Calculate

3 k^{2} - 5 k + 12 k - 20

Rewrite the expression

k \times 3 k - k \times 5 + 4 \times 3 k - 4 \times 5

Factor out k from the expression

k (3 k - 5) + 4 \times 3 k - 4 \times 5

Factor out 4 from the expression

k (3 k - 5) + 4 (3 k - 5)

Factor out 3 k - 5 from the expression

(k + 4) (3 k - 5)

(k + 4) (3 k - 5) = 0

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

3 k - 5 = 0 k + 4 = 0

Solve the equation for k

More Steps

Evaluate

3 k - 5 = 0

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

3 k = 0 + 5

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

3 k = 5

Divide both sides

\frac{3 k}{3} = \frac{5}{3}

Divide the numbers

k = \frac{5}{3}

k = \frac{5}{3} k + 4 = 0

Solve the equation for k

More Steps

Evaluate

k + 4 = 0

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

k = 0 - 4

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

k = - 4

k = \frac{5}{3} k = - 4

Solution

k_{1} = - 4, k_{2} = \frac{5}{3}

Alternative Form

k_{1} = - 4, k_{2} = 1. \dot{6}

Show Solution