Solve 3a^2-34a+80

Question

Factor the expression

(a - 8) (3 a - 10)

Evaluate

3 a^{2} - 34 a + 80

Rewrite the expression

3 a^{2} + (- 10 - 24) a + 80

Calculate

3 a^{2} - 10 a - 24 a + 80

Rewrite the expression

a \times 3 a - a \times 10 - 8 \times 3 a + 8 \times 10

Factor out a from the expression

a (3 a - 10) - 8 \times 3 a + 8 \times 10

Factor out - 8 from the expression

a (3 a - 10) - 8 (3 a - 10)

Solution

(a - 8) (3 a - 10)

Show Solution

a_{1} = \frac{10}{3}, a_{2} = 8

Alternative Form

a_{1} = 3. \dot{3}, a_{2} = 8

Evaluate

3 a^{2} - 34 a + 80

To find the roots of the expression,set the expression equal to 0

3 a^{2} - 34 a + 80 = 0

Factor the expression

More Steps

Evaluate

3 a^{2} - 34 a + 80

Rewrite the expression

3 a^{2} + (- 10 - 24) a + 80

Calculate

3 a^{2} - 10 a - 24 a + 80

Rewrite the expression

a \times 3 a - a \times 10 - 8 \times 3 a + 8 \times 10

Factor out a from the expression

a (3 a - 10) - 8 \times 3 a + 8 \times 10

Factor out - 8 from the expression

a (3 a - 10) - 8 (3 a - 10)

Factor out 3 a - 10 from the expression

(a - 8) (3 a - 10)

(a - 8) (3 a - 10) = 0

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

a - 8 = 0 3 a - 10 = 0

Solve the equation for a

More Steps

Evaluate

a - 8 = 0

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

a = 0 + 8

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

a = 8

a = 8 3 a - 10 = 0

Solve the equation for a

More Steps

Evaluate

3 a - 10 = 0

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

3 a = 0 + 10

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

3 a = 10

Divide both sides

\frac{3 a}{3} = \frac{10}{3}

Divide the numbers

a = \frac{10}{3}

a = 8 a = \frac{10}{3}

Solution

a_{1} = \frac{10}{3}, a_{2} = 8

Alternative Form

a_{1} = 3. \dot{3}, a_{2} = 8

Show Solution