1½ and -2⅓

The first root is $x_1 = 1 \frac{1}{2}$.

$$x_1 = \frac{1 \times 2 + 1}{2} = \frac{3}{2}$$

The second root is $x_2 = -2 \frac{1}{3}$.

$$x_2 = -\frac{2 \times 3 + 1}{3} = -\frac{7}{3}$$

$$x_1 + x_2 = \frac{3}{2} + \left(-\frac{7}{3}\right)$$

To add these fractions, find a common denominator, which is 6.

$$x_1 + x_2 = \frac{3 \times 3}{2 \times 3} - \frac{7 \times 2}{3 \times 2} = \frac{9}{6} - \frac{14}{6} = \frac{9 - 14}{6} = -\frac{5}{6}$$

$$x_1 x_2 = \left(\frac{3}{2}\right) \times \left(-\frac{7}{3}\right)$$ $$x_1 x_2 = -\frac{3 \times 7}{2 \times 3} = -\frac{21}{6}$$

Simplify the fraction by dividing the numerator and denominator by 3.

$$x_1 x_2 = -\frac{7}{2}$$

Substitute the sum and product of the roots into the formula.

$$x^2 - \left(-\frac{5}{6}\right)x + \left(-\frac{7}{2}\right) = 0$$ $$x^2 + \frac{5}{6}x - \frac{7}{2} = 0$$

$$6 \times \left(x^2 + \frac{5}{6}x - \frac{7}{2}\right) = 6 \times 0$$ $$6x^2 + 6 \times \frac{5}{6}x - 6 \times \frac{7}{2} = 0$$ $$6x^2 + 5x - 21 = 0$$