solve the quadratic equation 2x^4-3x^3-7x^2 12x-4=0

well, if you meant

2x^4-3x^3-7x^2+12x-4, it is a quartic, but can easily be factored into two quadratic factors.

It is (x^2-4)(2x^2-3x+1)

which are both easily solved.