Solve 6y^2-7y-20 = 0

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

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

Alternative Form

y_{1} = - 1. \dot{3}, y_{2} = 2.5

Evaluate

6 y^{2} - 7 y - 20 = 0

Factor the expression

More Steps

Evaluate

6 y^{2} - 7 y - 20

Rewrite the expression

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

Calculate

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

Rewrite the expression

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

Factor out 2 y from the expression

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

Factor out - 5 from the expression

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

Factor out 3 y + 4 from the expression

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

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

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

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

y = \frac{5}{2} 3 y + 4 = 0

Solve the equation for y

More Steps

Evaluate

3 y + 4 = 0

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

3 y = 0 - 4

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

3 y = - 4

Divide both sides

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

Divide the numbers

y = \frac{- 4}{3}

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

y = - \frac{4}{3}

y = \frac{5}{2} y = - \frac{4}{3}

Solution

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

Alternative Form

y_{1} = - 1. \dot{3}, y_{2} = 2.5

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