Describe the number and type of roots for the equation 2x^2+7=12x+4

Arrange into standard form
2x^2-12x+3=0

Use the discriminant to find the number of real roots
(-12)^2-4(2)(3)
144-8(3)
144-24
120

Because the discriminant is positive, it has 2 real roots.
Try to factor it, if it is not possible, the roots are irrational.

x^2-12x+6
Not factorable

Final 2 real, irrational roots