Solve 4t^2-5t-6=0

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

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

Alternative Form

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

Evaluate

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

Factor the expression

More Steps

Evaluate

4 t^{2} - 5 t - 6

Rewrite the expression

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

Calculate

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

Rewrite the expression

t \times 4 t + t \times 3 - 2 \times 4 t - 2 \times 3

Factor out t from the expression

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

Factor out - 2 from the expression

t (4 t + 3) - 2 (4 t + 3)

Factor out 4 t + 3 from the expression

(t - 2) (4 t + 3)

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

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

t - 2 = 0 4 t + 3 = 0

Solve the equation for t

More Steps

Evaluate

t - 2 = 0

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

t = 0 + 2

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

t = 2

t = 2 4 t + 3 = 0

Solve the equation for t

More Steps

Evaluate

4 t + 3 = 0

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

4 t = 0 - 3

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

4 t = - 3

Divide both sides

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

Divide the numbers

t = \frac{- 3}{4}

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

t = - \frac{3}{4}

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

Solution

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

Alternative Form

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

Show Solution