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 = [ -5 ± √((5)^2 - 4(-4)(-7)) ] / ( 2(-4) )
x = [-5 ± √(25 - (112) ) ] / ( -8 )
x = [-5 ± √(-87) ] / ( -8)
Since √-87 is nonreal, there are no real solutions to the given equation.