Question 303995
There should 4 solutions
10x^4-17x^2+3=0 
substitute z for x^2
10z^2-17z+3=0
factor
we want factors of 30 that add up to -17
-15 and -2
10z^2-15z-2z+3=0
5z*(2z-3)-1*(2z-3)=0
(5z-1)*(2z-3)=0
FOIL
10z^2-2z-15z+3=0
ok
plug x^2 back in for z
(5z-1)*(2z-3)=0
(5x^2-1)*(2x^2-3)=0
5x^2-1=0
5x^2=1
x^2=1/5
x=+-sqrt(1/5)

and 
2x^2-3=0
2x^2=3
x^2=3/2
x=+-sqrt(3/2)
x=+-sqrt(1/5)