Solve 15x^2-2x-8=0

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

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

Alternative Form

x_{1} = - 0. \dot{6}, x_{2} = 0.8

Evaluate

15 x^{2} - 2 x - 8 = 0

Factor the expression

More Steps

Evaluate

15 x^{2} - 2 x - 8

Rewrite the expression

15 x^{2} + (- 12 + 10) x - 8

Calculate

15 x^{2} - 12 x + 10 x - 8

Rewrite the expression

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

Factor out 3 x from the expression

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

Factor out 2 from the expression

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

Factor out 5 x - 4 from the expression

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

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

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

5 x - 4 = 0 3 x + 2 = 0

Solve the equation for x

More Steps

Evaluate

5 x - 4 = 0

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

5 x = 0 + 4

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

5 x = 4

Divide both sides

\frac{5 x}{5} = \frac{4}{5}

Divide the numbers

x = \frac{4}{5}

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

Solve the equation for x

More Steps

Evaluate

3 x + 2 = 0

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

3 x = 0 - 2

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

3 x = - 2

Divide both sides

\frac{3 x}{3} = \frac{- 2}{3}

Divide the numbers

x = \frac{- 2}{3}

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

x = - \frac{2}{3}

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

Solution

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

Alternative Form

x_{1} = - 0. \dot{6}, x_{2} = 0.8

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