I have an equation sqrt(x+1)+sqrt(x+2)+2*sqrt((x+1)*(x+2))+2*x-3=0. Now I want to introduce new variable t = t=sqrt(x+1)+sqrt(x+2). How must I do?

I did

f:=x->sqrt(x+1)+sqrt(x+2)+2*sqrt((x+1)*(x+2))+2*x-3:

sol:=solve(t=sqrt(x+1)+sqrt(x+2),x):

A:=f(sol):
simplify(A);

But I did not receive a good answer. Please help me.  

I want to make a triangle with its sides: 3, 4, 5. My code can not  run. Please help me. 

> restart:

ListTools[Categorize]:

N:=10:

L:=[]:

for x1 to N do

for y1 from x1 to N do

for z1 from y1 to N do

for x2 to N do

for y2 to N do

I created a triangle whose length of the medians are integral numbers. Please comment to me about my code.

> resrart:

ListTools[Categorize]:

N:=5:

L:=[]:

for x1 from -N to N do

for y1 from x1 to N do

for z1 from y1 to N do

for x2 from -N to N do

for y2 from -N to N do

I want to find the first term and the common difference of the arithmetic progression (un) with the following condintions u7 + u15 = 60 and (u4)^2 + (u12)^2 = 1170, but i can not the code. Please help me. Thank you.

In geom3d, how can i make a triangle which coordinates of the center circle circumscribed triangle are integer numbers? Please help me. Thank you.