Respuesta :
The discriminant is the stuff under the square root in the quadratic equation. Let's first get this equation in standard form. This must equal 0! Let's see what we have:
[tex] 3-4x=-6x^2[/tex]
Since we need this quadratic to equal 0 to use the quadratic formula, add [tex] 6x^2 [/tex] to both sides.
[tex] 6x^2-4x+3=0[/tex]
Note that I just rearranged the -4 and +3 to make it in the [tex] ax^2+bx+c [/tex] form. Now, let's put this in the quadratic equation.
[tex]x=\frac{4 +\sqrt{(-4)^2-4(6)(3)} }{2(6)}[/tex]
Since we are only solving for the discriminant, let's simplify the expression under the square root.
[tex]\sqrt{(-4)^2-4(6)(3)}[/tex]
[tex]\sqrt{16-72}[/tex]
[tex]\sqrt{-56}[/tex]
Now, since we have a negative number in the discriminant, we know that neither of the solutions will be real numbers. They will be in terms of [tex] i [/tex] ([tex] i=\sqrt{-1}[/tex])
The simplified version of the discriminant is:
[tex] 2i\sqrt{14}[/tex]
However, if you have not learned imaginary numbers yet, you can say the discriminant is -56.
