solve 4x^3-6x+2=0 for all x

Answer 1

2x^3 -3x +1 = 0
x = 1 is one solution. That is obvious by inspection. Therefore (x-1) is a factor of the equation.
Divide the cubic by (x-1) to get the quadratic factor, (2x^2 +2x -1). That can be solved using the quadratic equation to get the other two roots
x = (1/4)[-2 +/- sqrt 12]
= -(1/2) +/- (1/2)sqrt3

Answer 2

by the way, this is algebra, not aclculus

Answer 3

this is part of calculus cause i need it to find critical points of a graph