Solve 3x^(2)-5x-12=0

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = - \frac{4}{3}, x_{2} = 3

Alternative Form

x_{1} = - 1. \dot{3}, x_{2} = 3

Evaluate

3 x^{2} - 5 x - 12 = 0

Factor the expression

More Steps

Evaluate

3 x^{2} - 5 x - 12

Rewrite the expression

3 x^{2} + (4 - 9) x - 12

Calculate

3 x^{2} + 4 x - 9 x - 12

Rewrite the expression

x \times 3 x + x \times 4 - 3 \times 3 x - 3 \times 4

Factor out x from the expression

x (3 x + 4) - 3 \times 3 x - 3 \times 4

Factor out - 3 from the expression

x (3 x + 4) - 3 (3 x + 4)

Factor out 3 x + 4 from the expression

(x - 3) (3 x + 4)

(x - 3) (3 x + 4) = 0

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

x - 3 = 0 3 x + 4 = 0

Solve the equation for x

More Steps

Evaluate

x - 3 = 0

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

x = 0 + 3

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

x = 3

x = 3 3 x + 4 = 0

Solve the equation for x

More Steps

Evaluate

3 x + 4 = 0

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

3 x = 0 - 4

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

3 x = - 4

Divide both sides

\frac{3 x}{3} = \frac{- 4}{3}

Divide the numbers

x = \frac{- 4}{3}

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

x = - \frac{4}{3}

x = 3 x = - \frac{4}{3}

Solution

x_{1} = - \frac{4}{3}, x_{2} = 3

Alternative Form

x_{1} = - 1. \dot{3}, x_{2} = 3

Show Solution