The discriminant of an equation ax^2 + bx + c = 0 is b^2 - 4ac

Here we have x^2+11x+121=x+96

=> x^2 + 10x +25 = 0

b^2 - 4ac = 100 - 100 = 0

**The discriminant is 0.**

`x^2+11x+121=x+96` combine the like terms

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

`x^2+10x+25=0 ` to find the discminant use the formula `b^2-4ac`

`a=1` `b=10 ` `c=25 ` plug it in

`10^2-4(1)(25) ` simplify

`100-100` make an equation

`100-100=0` so the discriminant is 0, this means the problem has 1 real solution

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.**