Solve the equation for x, where x is a real number (5 points): -13x^2 + 13x + 39 = 34

Subtract 34 to both sides so that the equation becomes -13x^2 + 13x + 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 = [ -13 ± √((13)^2 - 4(-13)(5)) ] / ( 2(-13) )
                           x = [-13 ± √(169 - (-260) ) ] / ( -26 )
                           x = [-13 ± √(429) ] / ( -26)
                           x = [-13 ± sqrt(429) ] / ( -26 )
                           x = 1/2 ± -sqrt(429)/26
The answers are 1/2 + sqrt(429)/26 and 1/2 - sqrt(429)/26.