Chapter 8 - Section 8.1 - The Square Root Property and Completing the Square - Exercise Set - Page 596: 117

$3x^2 + 4x + 2 = 0$ $b^2 - 4ac = -8$

$3 + \frac{4}{x} = -\frac{2}{x^2}$ Add $\frac{2}{x^2}$ on both sides. $3 + \frac{4}{x} +\frac{2}{x^2}= -\frac{2}{x^2}+\frac{2}{x^2}$ $3 + \frac{4}{x} +\frac{2}{x^2}= 0$ Multiply both sides by $x^2$. $(3 + \frac{4}{x} +\frac{2}{x^2})(x^2)= 0⋅x^2$ $3x^2 + 4x + 2 = 0$ $a = 3$ $b = 4$ $c = 2$ $b^2 - 4ac = (4^2)-4(3)(2)$ $b^2 - 4ac = -8$