The quadratic formula is used for a quadratic equation of the form ax^2 + bx + c = 0 when it is not possible or very difficult to factorize the expression ax^2 + bx + c.
Here, to find the roots x1 and x2 which are usually irrational or complex we use the following relations:
x1 = [-b + sqrt (b^2 - 4ac)]/2a
x2 = [-b - sqrt (b^2 - 4ac)]/2a
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