We have to find the discriminant of x^2+11x+121=x+96.

Now discriminant of ax^2 + bx + c = 0 is given by b^2 - 4ac.

x^2+11x+121=x+96

=> x^2 + 11x - x + 121 -96 = 0

=> x^2 + 10 x - 25

so a = 1 , b = 10 and c = 25

The discriminant is 10^2 - 4*1*25

= 100 - 100 = 0

**Therefore the discriminant is 0.**

First of all, you need to set up the problem into the `ax^2 + bx + c`

`x^2 + 11 x + 121 = x + 96`

`x^2 + 11x + 35 = x` Subtract 96 from both sides

`x^2 + 10x + 35 = 0` Subtracting x to both sides to make it in the proper form.

Now we must distinguish which is a, b, and c

`a = 1`

`b = 10`

`c = 35` The discriminant formula is `b^2 - 4ac`

`(10)^2 - 4(1)(35)`

`100 - 140`

`= -140`

**After plugging it into the equation, our discriminant is -140. When graphing, this means there are no real roots.**

The given equation is x^2+11x+121=x+96.

Before finding the discriminant of the equation, we write the equation in the standard form ax^2+bx+c= o whose discriminant D is given by: D = (b^2-4ac).

x^2+11x+121=x+96 is rearranged as: x^2+11x+121-x-96.

=> x^2 +10x +25, which is like ax^2+bx+c.

=> a=1, b= 10 and c= 25.

So D = b^2-4ac = (10^2-4*1*25) = 0.

So the discriminant of the given equation is **0**.

Before determining the discriminant, we'll move all terms to the left side:

x^2+11x+121-x-96 = 0

We'll combine like terms:

x^2 + 10x + 25 = 0

We'll write the formula of discriminant:

delta = b^2 - 4ac

We'll identify the coefficients a,b,c:

a = 1, b = 10 , c = 25

delta = 100 - 4*25

delta = 100 - 100

**delta = 0**

**The discriminant of quadratic equation is delta = 0.**