Determine the roots of the equation x^2-5x+6=0.

We'll apply the quadratic
formula

The original equation is:
x^2-5x+6=0

x1 = [-b + sqrt(b^2 -
4ac)]/2a

We'll identify the
coefficients:

a = 1

b =
-5

c = 6

b^2 - 4ac = (-5)^2 -
4*1*6 = 25 - 24

sqrt(b^2 - 4ac) = sqrt(25 -
24)

sqrt(b^2 - 4ac) = 1

We'll
substitute in the formula:

x1 = [-(-5) + sqrt(25 -
24)]/2

x1 = (5+1)/2

x1 =
3

x2 = (5-1)/2

x2 =
2

The roots of the equation are {2 ;
3}.