Solve the equation for x, where x is a real number (5 points): 2x^2 + 15x + 4 = 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 = [ -15 ± √((15)^2 - 4(2)(4)) ] / ( 2(2) )
                           x = [-15 ± √(225 - (32) ) ] / ( 4 )
                           x = [-15 ± √(193) ] / ( 4)
                           x = [-15 ± sqrt(193) ] / ( 4 )
                           x = -15/4 ± sqrt(193)/4
The answers are -15/4 + sqrt(193)/4 and -15/4 - sqrt(193)/4.