Recall that the "discriminat" of a quadratic equation of the form:
a x^2 + b x + c = 0
is given by the formula: b^2 - 4 a c
So for our equation:
x^2 - 5 x = -2, we start by adding 2 to both sides, in order to get the appropriate form equal to zero:
x^2 - 5 x + 2 = 0
Now we recognize:
a = 1
b = - 5
c = 2
and write the discriminant
b^2 - 4 a c = (-5)^2 - 4 (1) (2) = 25 - 8 = 17
Then, the discriminat of the equation is: 17.