how do i factor this using the quadratic equation 21x^2+22x-8=0

We can also use the quadratic formula to factorize the
equation:

21x^2+22x-8=0

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

We'll identify the coefficients
a,b,c:

a = 21

b =
22

c = -8

b^2 - 4ac = 484 +
672

sqrt (b^2 - 4ac) = sqrt
1156

sqrt (b^2 - 4ac) = 34

x1
= (-22+34)/2*21

x1 = 12/42

x1
= 6/21

x2 =  (-22-34)/2*21

x2
= -56/42

x2 = -28/21

We can
now factorize the quadratic:

21x^2+22x-8 = 21(x - x1)(x -
x2)

We'll substitute x1 and
x2

21x^2+22x-8 = 21(x - 6/21)(x +
28/21)

or

21x^2+22x-8
= (21x - 6)(21x + 28)