Solve the equation for x, where x is a real number (5 points): -2x^2 + 5x - 10 = 3

Subtract 3 from both sides so that the equation becomes -2x^2 + 5x - 13 = 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 = [ -5 ± √((5)^2 - 4(-2)(-13)) ] / ( 2(-2) )
                                      x = [-5 ± √(25 - (104) ) ] / ( -4 )
                                      x = [-5 ± √(-79) ] / ( -4)
Since √-79 is nonreal, the answer to this question is that there are no real solutions.