Solve 4y^(2)-7y-15=0

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

y_{1} = - \frac{5}{4}, y_{2} = 3

Alternative Form

y_{1} = - 1.25, y_{2} = 3

Evaluate

4 y^{2} - 7 y - 15 = 0

Factor the expression

More Steps

Evaluate

4 y^{2} - 7 y - 15

Rewrite the expression

4 y^{2} + (5 - 12) y - 15

Calculate

4 y^{2} + 5 y - 12 y - 15

Rewrite the expression

y \times 4 y + y \times 5 - 3 \times 4 y - 3 \times 5

Factor out y from the expression

y (4 y + 5) - 3 \times 4 y - 3 \times 5

Factor out - 3 from the expression

y (4 y + 5) - 3 (4 y + 5)

Factor out 4 y + 5 from the expression

(y - 3) (4 y + 5)

(y - 3) (4 y + 5) = 0

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

y - 3 = 0 4 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 4 y + 5 = 0

Solve the equation for y

More Steps

Evaluate

4 y + 5 = 0

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

4 y = 0 - 5

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

4 y = - 5

Divide both sides

\frac{4 y}{4} = \frac{- 5}{4}

Divide the numbers

y = \frac{- 5}{4}

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

y = - \frac{5}{4}

y = 3 y = - \frac{5}{4}

Solution

y_{1} = - \frac{5}{4}, y_{2} = 3

Alternative Form

y_{1} = - 1.25, y_{2} = 3

Show Solution