Given the quadratic equation:

x^2 + 7x + 9 = 0

We need to solve for the roots using the quadratic formula.

Then we know that:

a =1 b= 7 c = 9

The formula for the roots is:

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

==> x1= ( -7 + sqrt(49 -4*1*9) / 2

= (-7 + sqrt(13) / 2

==>** x1= (-7/2) + sqrt13 / 2**

**==> x2= (-7/2) - sqrt13 /2**

We know that the quadratic formula for finding the roots of the quadratic equation is:

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

x2 = [-b - sqrt(b^2 - 4ac)]/2a

We know that the expression under the square root is called the discriminant of the quadratic, delta.

If delta is positive, the equation has 2 real distinc roots.

If delta is zero, the equation has 2 equal real roots.

We'll compute delta. For this reason, we'll identify a,b,c:

a = 1 , b = 7 , c = 9

delta = 49 - 36

delta = 13 > 0

Since delta is positive, the equtaion has 2 real distinct roots:

**x1 = (-7+sqrt 13)/2**

**x2 = (-7-sqrt 13)/2**