Solve the equation for x, where x is a real number (5 points): -4x^2 + 3x - 1 = 2

Subtract 2 to both sides so that the equation becomes -4x^2 + 3x - 3 = 0.
To find the solutions to this equation, we can apply the quadratic formula. This quadratic formula solves equations of the form ax^2 + bx + c = 0
                                     x = [ -b ± √(b^2 - 4ac) ] / (2a)
                                     x = [ -3 ± √((3)^2 - 4(-4)(-3)) ] / ( 2(-4) )
                                     x = [-3 ± √(9 - (48) ) ] / ( -8 )
                                     x = [-3 ± √(-39) ] / ( -8)
The answers to this question is that there are no real solutions since the discriminant is -39. √-39 is nonreal.