how do i solve the equation 34x^4-85x^3+51x^2=0
You can factor out x^2. That already tells you that x=0 is a solution. That leaves you with 17(2x^2 +5 x^ +3) = 0
The 17 is not zero,
2x^2 +5 x^ +3 = 0
(x +1)(2x + 3) = 0
You can probably guess what the next step is.