Solve the equation for x, where x is a real number (5 points): 2x^2 + 8x + 3 = 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 = [ -8 ± √((8)^2 - 4(2)(3)) ] / ( 2(2) )
                                           x = [-8 ± √(64 - (24) ) ] / ( 4 )
                                           x = [-8 ± √(40) ] / ( 4)
                                           x = [-8 ± 2*sqrt(10) ] / ( 4 )
                                           x = -2 ± sqrt(10)/2
The answers are -2 + sqrt(10)/2 and -2 - sqrt(10)/2.