Quadratic equations again

can comeone please tell me why does the solution of the following equation not use the standard quadratic formula?

the question is

Given that the equation has repeated root calculate the possible values of the constant k

I solved for the discriminant =0, but when i was applying the quadratic formula to the simplified equation of the discriminant, and then tried to use the quadratic formula to solve it, nothing sensible came out. I graphed the equation and found out, that it gives the correct roots only when divided by a and not by 2a as is in the quadratic formula?

Can someone please help me?

Thank you!