Determine the value of k for which the quadratic . . .

Problem : Determine the value of k for which the quadratic equation has equal roots. (k-12)x²+2(k-12)x+2=0

Doubt by Ananya

Solution : (k-12)x²+2(k-12)x+2=0
a = k-12
b = 2(k-12)
c= 2
Roots are equal (Given)
∴ D = 0

D = b²-4ac
0 = [2(k-12)]² - 4(k-12)(2)
0 = 4(k-12)² - 8(k-12)
0 = 4(k-12) (k-12-2)
0 = 4(k-12) (k-14)
0 = (k-12) (k-14)

k-12 = 0 OR k-14 = 0
k = 12  OR K = 14

but k ≠ 12
∵ a ≠ 0

∴ a = 14