Solve 6x^2-5x-6=0

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

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

Alternative Form

x_{1} = - 0. \dot{6}, x_{2} = 1.5

Evaluate

6 x^{2} - 5 x - 6 = 0

Factor the expression

More Steps

Evaluate

6 x^{2} - 5 x - 6

Rewrite the expression

6 x^{2} + (4 - 9) x - 6

Calculate

6 x^{2} + 4 x - 9 x - 6

Rewrite the expression

2 x \times 3 x + 2 x \times 2 - 3 \times 3 x - 3 \times 2

Factor out 2 x from the expression

2 x (3 x + 2) - 3 \times 3 x - 3 \times 2

Factor out - 3 from the expression

2 x (3 x + 2) - 3 (3 x + 2)

Factor out 3 x + 2 from the expression

(2 x - 3) (3 x + 2)

(2 x - 3) (3 x + 2) = 0

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

2 x - 3 = 0 3 x + 2 = 0

Solve the equation for x

More Steps

Evaluate

2 x - 3 = 0

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

2 x = 0 + 3

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

2 x = 3

Divide both sides

\frac{2 x}{2} = \frac{3}{2}

Divide the numbers

x = \frac{3}{2}

x = \frac{3}{2} 3 x + 2 = 0

Solve the equation for x

More Steps

Evaluate

3 x + 2 = 0

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

3 x = 0 - 2

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

3 x = - 2

Divide both sides

\frac{3 x}{3} = \frac{- 2}{3}

Divide the numbers

x = \frac{- 2}{3}

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

x = - \frac{2}{3}

x = \frac{3}{2} x = - \frac{2}{3}

Solution

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

Alternative Form

x_{1} = - 0. \dot{6}, x_{2} = 1.5

Show Solution