In simplest radical form what are the solutions to the quadratic equation 0=-3x^2-4x+5

This is a quadratic equation with coefficients a= -3, b= -4 and c= 5.  Thus, the discriminant  b^2-4ac is      (-4)^2 - 4(-3)(-4)  =  16-48 = 16(1-3) = 16(-2).

The solutions are
       -(-4) plus or minus sqrt(discriminant)
x =
                        2(-3)
          4 plus or minus sqrt(16[-2])
   =
                           -6
         4 plus or minus 4*i*sqrt[2]
   =
                            -6

This reduces to:
 
       -2  plus or minus i*2*sqrt[2]
x =             (answers)
                     3