Solve the equation for x, where x is a real number (5 points): 3x^2 + 2x + 15 = 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 = [-2 ± √((2)^2 - 4(3)(15)) ] / ( 2(3) )
                                      x = [-2 ± √(4- (180) ) ] / ( 6 )
                                      x = [-2 ± √(-176) ] / ( 6)
Since √-176 is nonreal, the answer to this question is that there are no real solutions.