Solve 10y^2 - 11y - 6 = 0

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

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

Alternative Form

y_{1} = - 0.4, y_{2} = 1.5

Evaluate

10 y^{2} - 11 y - 6 = 0

Factor the expression

More Steps

Evaluate

10 y^{2} - 11 y - 6

Rewrite the expression

10 y^{2} + (4 - 15) y - 6

Calculate

10 y^{2} + 4 y - 15 y - 6

Rewrite the expression

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

Factor out 2 y from the expression

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

Factor out - 3 from the expression

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

Factor out 5 y + 2 from the expression

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

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

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

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

Solve the equation for y

More Steps

Evaluate

2 y - 3 = 0

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

2 y = 0 + 3

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

2 y = 3

Divide both sides

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

Divide the numbers

y = \frac{3}{2}

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

Solve the equation for y

More Steps

Evaluate

5 y + 2 = 0

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

5 y = 0 - 2

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

5 y = - 2

Divide both sides

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

Divide the numbers

y = \frac{- 2}{5}

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

y = - \frac{2}{5}

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

Solution

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

Alternative Form

y_{1} = - 0.4, y_{2} = 1.5

Show Solution