We need the roots of the equation before building the sign chart
#2x^2-8x+3=0#
We calculate the discriminant
#Delta=b^2-4ac=(-8)^2-4(2)(3)#
#=64-24=40#
#Delta>0#, there are 2 real roots
#x_1=(8-sqrt40)/4=(4-sqrt10)/2#
#x_2=(8+sqrt40)/4=(4+sqrt10)/2#
Let #f(x)=(x-x_1)(x-x_2)#
We can, now, build the sign chart
#color(white)(aaaa)##x##color(white)(aaaaaa)##-oo##color(white)(aaaa)##x_1##color(white)(aaaa)##x_2##color(white)(aaaa)##+oo#
#color(white)(aaaa)##x-x_1##color(white)(aaaaaa)##-##color(white)(aaaa)##+##color(white)(aaaa)##+#
#color(white)(aaaa)##x-x_2##color(white)(aaaaaa)##-##color(white)(aaaa)##-##color(white)(aaaa)##+#
#color(white)(aaaa)##f(x)##color(white)(aaaaaaaa)##+##color(white)(aaaa)##-##color(white)(aaaa)##+#
Therefore,
#f(x)<0# when #x in ]x_1,x_2[#, #=>#
#x in ](4-sqrt10)/2, (4+sqrt10)/2[#