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 $\displaystyle (4k+1)x^2-(k+10)x+2k=0 $ 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!