Solve 2x^2+(5/3) x - 2 = 0

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

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

Alternative Form

x_{1} = - 1.5, x_{2} = 0. \dot{6}

Evaluate

2 x^{2} + \frac{5}{3} x - 2 = 0

Factor the expression

More Steps

Evaluate

2 x^{2} + \frac{5}{3} x - 2

Rewrite the expression

\frac{1}{3} \times 6 x^{2} + \frac{1}{3} \times 5 x - \frac{1}{3} \times 6

Factor out \frac{1}{3} from the expression

\frac{1}{3} (6 x^{2} + 5 x - 6)

Factor the expression

More Steps

Evaluate

6 x^{2} + 5 x - 6

Rewrite the expression

6 x^{2} + (- 4 + 9) x - 6

Calculate

6 x^{2} - 4 x + 9 x - 6

Rewrite the expression

2 x \times 3 x - 2 x \times 2 + 3 \times 3 x - 3 \times 2

Factor out 2 x from the expression

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

Factor out 3 from the expression

2 x (3 x - 2) + 3 (3 x - 2)

Factor out 3 x - 2 from the expression

(2 x + 3) (3 x - 2)

\frac{1}{3} (2 x + 3) (3 x - 2)

\frac{1}{3} (2 x + 3) (3 x - 2) = 0

Divide the terms

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

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

3 x - 2 = 0 2 x + 3 = 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}

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

Solve the equation for x

More Steps

Evaluate

2 x + 3 = 0

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

2 x = 0 - 3

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

2 x = - 3

Divide both sides

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

Divide the numbers

x = \frac{- 3}{2}

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

x = - \frac{3}{2}

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

Solution

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

Alternative Form

x_{1} = - 1.5, x_{2} = 0. \dot{6}

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