Solve 9a^2 - 30 = 3a

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

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

Alternative Form

a_{1} = - 1. \dot{6}, a_{2} = 2

Evaluate

9 a^{2} - 30 = 3 a

Move the expression to the left side

9 a^{2} - 30 - 3 a = 0

Factor the expression

More Steps

Evaluate

9 a^{2} - 30 - 3 a

Evaluate

9 a^{2} - 3 a - 30

Rewrite the expression

3 \times 3 a^{2} - 3 a - 3 \times 10

Factor out 3 from the expression

3 (3 a^{2} - a - 10)

Factor the expression

More Steps

Evaluate

3 a^{2} - a - 10

Rewrite the expression

3 a^{2} + (5 - 6) a - 10

Calculate

3 a^{2} + 5 a - 6 a - 10

Rewrite the expression

a \times 3 a + a \times 5 - 2 \times 3 a - 2 \times 5

Factor out a from the expression

a (3 a + 5) - 2 \times 3 a - 2 \times 5

Factor out - 2 from the expression

a (3 a + 5) - 2 (3 a + 5)

Factor out 3 a + 5 from the expression

(a - 2) (3 a + 5)

3 (a - 2) (3 a + 5)

3 (a - 2) (3 a + 5) = 0

Divide the terms

(a - 2) (3 a + 5) = 0

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

a - 2 = 0 3 a + 5 = 0

Solve the equation for a

More Steps

Evaluate

a - 2 = 0

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

a = 0 + 2

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

a = 2

a = 2 3 a + 5 = 0

Solve the equation for a

More Steps

Evaluate

3 a + 5 = 0

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

3 a = 0 - 5

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

3 a = - 5

Divide both sides

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

Divide the numbers

a = \frac{- 5}{3}

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

a = - \frac{5}{3}

a = 2 a = - \frac{5}{3}

Solution

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

Alternative Form

a_{1} = - 1. \dot{6}, a_{2} = 2

Show Solution