Chapter 1 - Section 1.3 - Complex Numbers; Quadratic Equations in the Complex Number System - 1.3 Assess Your Understanding - Page 112: 77

The two solutions are real (and not equal to each other).

$2x^{2}+3x=4$ $2x^{2}+3x-4=0$ To determine the nature of the solutions (without solving), we compute the sign of the discriminant in the quadratic formula ($a=2,\ b=3,\ c=-4$): $b^{2}-4ac=3^{2}-4*2*-4=9+32=41$ Since the discriminant is positive, the two solutions are real (and not equal to each other).