Solve 2y^2-y-15=0

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

y_{1} = - \frac{5}{2}, y_{2} = 3

Alternative Form

y_{1} = - 2.5, y_{2} = 3

Evaluate

2 y^{2} - y - 15 = 0

Factor the expression

More Steps

Evaluate

2 y^{2} - y - 15

Rewrite the expression

2 y^{2} + (5 - 6) y - 15

Calculate

2 y^{2} + 5 y - 6 y - 15

Rewrite the expression

y \times 2 y + y \times 5 - 3 \times 2 y - 3 \times 5

Factor out y from the expression

y (2 y + 5) - 3 \times 2 y - 3 \times 5

Factor out - 3 from the expression

y (2 y + 5) - 3 (2 y + 5)

Factor out 2 y + 5 from the expression

(y - 3) (2 y + 5)

(y - 3) (2 y + 5) = 0

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

y - 3 = 0 2 y + 5 = 0

Solve the equation for y

More Steps

Evaluate

y - 3 = 0

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

y = 0 + 3

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

y = 3

y = 3 2 y + 5 = 0

Solve the equation for y

More Steps

Evaluate

2 y + 5 = 0

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

2 y = 0 - 5

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

2 y = - 5

Divide both sides

\frac{2 y}{2} = \frac{- 5}{2}

Divide the numbers

y = \frac{- 5}{2}

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

y = - \frac{5}{2}

y = 3 y = - \frac{5}{2}

Solution

y_{1} = - \frac{5}{2}, y_{2} = 3

Alternative Form

y_{1} = - 2.5, y_{2} = 3

Show Solution