Solve the equation for x, where x is a real number (5 points): -13x^2 + 17x + 39 = 44

We first subtract 44 from both sides so that the equation becomes -13x^2 + 17x - 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 = [ -17 ± √(17^2 - 4(-13)(-5)) ] / ( 2(-13) )
                     x = [ -17 ± √(289 - (260) ) ] / ( -26 )
                     x = [ -17 ± √(29) ] / ( -26)
                     x = [ -17 ± sqrt(29) ] / ( -26 )
                     x = 17/26 ± -sqrt(29)/26
The answers are 17/26 + sqrt(29)/26 and 17/26 - sqrt(29)/26.