we know that
The discriminant of the quadratic equation of the form
[tex] ax^{2} +bx+c=0 [/tex]
is equal to [tex] (b^{2}-4ac ) [/tex]
we have
[tex] 3 -4x = -6x^{2} [/tex]
[tex] 3 -4x = -6x^{2} \\ -6x^{2}+4x-3=0 [/tex]
in this problem
[tex] a=-6\\ b=4\\ c=-3 [/tex]
Substitute in the formula of discriminant
[tex] (b^{2}-4ac )=4^{2}-4*(-6)*(-3)\\ =16-4*18\\ =-56 [/tex]
therefore
the answer is
the discriminant of the quadratic equation is [tex] -56 [/tex]
