Solve 8t^2 -26t+15= 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} = \frac{5}{2}

Alternative Form

t_{1} = 0.75, t_{2} = 2.5

Evaluate

8 t^{2} - 26 t + 15 = 0

Factor the expression

More Steps

Evaluate

8 t^{2} - 26 t + 15

Rewrite the expression

8 t^{2} + (- 6 - 20) t + 15

Calculate

8 t^{2} - 6 t - 20 t + 15

Rewrite the expression

2 t \times 4 t - 2 t \times 3 - 5 \times 4 t + 5 \times 3

Factor out 2 t from the expression

2 t (4 t - 3) - 5 \times 4 t + 5 \times 3

Factor out - 5 from the expression

2 t (4 t - 3) - 5 (4 t - 3)

Factor out 4 t - 3 from the expression

(2 t - 5) (4 t - 3)

(2 t - 5) (4 t - 3) = 0

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

2 t - 5 = 0 4 t - 3 = 0

Solve the equation for t

More Steps

Evaluate

2 t - 5 = 0

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

2 t = 0 + 5

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

2 t = 5

Divide both sides

\frac{2 t}{2} = \frac{5}{2}

Divide the numbers

t = \frac{5}{2}

t = \frac{5}{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}

t = \frac{5}{2} t = \frac{3}{4}

Solution

t_{1} = \frac{3}{4}, t_{2} = \frac{5}{2}

Alternative Form

t_{1} = 0.75, t_{2} = 2.5

Show Solution