Solve 12x^2-4x-5=0

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = - \frac{1}{2}, x_{2} = \frac{5}{6}

Alternative Form

x_{1} = - 0.5, x_{2} = 0.8 \dot{3}

Evaluate

12 x^{2} - 4 x - 5 = 0

Factor the expression

More Steps

Evaluate

12 x^{2} - 4 x - 5

Rewrite the expression

12 x^{2} + (- 10 + 6) x - 5

Calculate

12 x^{2} - 10 x + 6 x - 5

Rewrite the expression

2 x \times 6 x - 2 x \times 5 + 6 x - 5

Factor out 2 x from the expression

2 x (6 x - 5) + 6 x - 5

Factor out 6 x - 5 from the expression

(2 x + 1) (6 x - 5)

(2 x + 1) (6 x - 5) = 0

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

6 x - 5 = 0 2 x + 1 = 0

Solve the equation for x

More Steps

Evaluate

6 x - 5 = 0

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

6 x = 0 + 5

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

6 x = 5

Divide both sides

\frac{6 x}{6} = \frac{5}{6}

Divide the numbers

x = \frac{5}{6}

x = \frac{5}{6} 2 x + 1 = 0

Solve the equation for x

More Steps

Evaluate

2 x + 1 = 0

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

2 x = 0 - 1

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

2 x = - 1

Divide both sides

\frac{2 x}{2} = \frac{- 1}{2}

Divide the numbers

x = \frac{- 1}{2}

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

x = - \frac{1}{2}

x = \frac{5}{6} x = - \frac{1}{2}

Solution

x_{1} = - \frac{1}{2}, x_{2} = \frac{5}{6}

Alternative Form

x_{1} = - 0.5, x_{2} = 0.8 \dot{3}

Show Solution