Solve the equation for x, where x is a real number: -3x^2 + 4x - 5 = 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 = [ -4 ± √((4)^2 - 4(-3)(-5)) ] / ( 2(-3) )
                                    x = [-4 ± √(16 - (60) ) ] / ( -6 )
                                    x = [-4 ± √(-44) ] / ( -6)
Since √-44 is nonreal, the answer to this question is that there are no real solutions.