For one and only 1 real solution, the discriminant = 0 (see chart attached)
So we know b^2-4ac=0 when the equation is in the format of ax^2+bx-c=0. Make sure your equation is in the right format first!
Given kx^2+12x-4=0
b=12
so b^2-4ac=0
144 = 4ac
144 = 4(k)(-4)
144/(-16) = k
k = -9