quick algebra question please?

imagine the length of longer leg equal x . The length of hypotenuse will be 3+x

& the length of shorter leg will be x-6

Now according of Pythagoras rule we have this sentence : ( 3+x )^2 = (x)^2 + ( x-6 )^2

Now solve the sentence like below :

( 3+x )^2 = (x)^2 + ( x-6 )^2

------> 9 + x^2 + 6x = x^2 + x^2 - 12x + 36

------> x^2 - 18x - 27 = 0

------> solve the Equation : ( 18 ± (radical ( 324 + 108 )) / 2

------> x have to two answers but in geometry we just accept positive answers,

and that answer is x = 19.35

So long leg is 19.35 , short leg is 13.35 & hypotenuse is 22.35

H=3+L

L=6+2S

where H=hypotenuse, L=long leg, S=short leg.

Since it's a right triangle, then

L^2+S^2=H^2

Put all lengths in terms of S.

(6+2S)^2+S^2=(3+6+2S)^2

(36+24S+4S^2)+S^2=(81+36S+4S^2)

5S^2+24S+36=4S^2+36S+81

S^2-12S-45=0

(S-15)(S+3)=0

S=-3, 15

Since S is a length, a negative value would not make sense.

S=15

L=6+2S=36

H=3+L=39