Solve 4x^(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{3}{4}, x_{2} = 2

Alternative Form

x_{1} = - 0.75, x_{2} = 2

Evaluate

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

Factor the expression

More Steps

Evaluate

4 x^{2} - 5 x - 6

Rewrite the expression

4 x^{2} + (3 - 8) x - 6

Calculate

4 x^{2} + 3 x - 8 x - 6

Rewrite the expression

x \times 4 x + x \times 3 - 2 \times 4 x - 2 \times 3

Factor out x from the expression

x (4 x + 3) - 2 \times 4 x - 2 \times 3

Factor out - 2 from the expression

x (4 x + 3) - 2 (4 x + 3)

Factor out 4 x + 3 from the expression

(x - 2) (4 x + 3)

(x - 2) (4 x + 3) = 0

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

x - 2 = 0 4 x + 3 = 0

Solve the equation for x

More Steps

Evaluate

x - 2 = 0

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

x = 0 + 2

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

x = 2

x = 2 4 x + 3 = 0

Solve the equation for x

More Steps

Evaluate

4 x + 3 = 0

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

4 x = 0 - 3

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

4 x = - 3

Divide both sides

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

Divide the numbers

x = \frac{- 3}{4}

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

x = - \frac{3}{4}

x = 2 x = - \frac{3}{4}

Solution

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

Alternative Form

x_{1} = - 0.75, x_{2} = 2

Show Solution