Use the discriminate to determine the number and the nature of the solutions of the giving equation.

4x^2+12x=7

Since b^2 - 4ac = 256 we have 2 real distinct root roots

Step-by-step explanation:

4x^2+12x=7

We need to subtract 7 to get it in the proper form

4x^2+12x-7=7-7

4x^2+12x-7=0

The discriminant is b^2 - 4ac

when the equation is ax^2 + bx+c

so a = 4 b=12 and c=-7

(12) ^2 - 4 (4) (-7)

144 + 112

256

If b^2 - 4ac > 0 we have 2 real distinct roots

If b^2 - 4ac = 0 we have one real root

If b^2 - 4ac < 0 we have two complex root

Since b^2 - 4ac = 256 we have 2 real distinct root roots