So x times y=15
x+y=12
solve
x+y=12
subtract x from both sides
y=12-x
subsitute
xy=15
x(12-x)=15
distribute
12x-x^2=15
subtract (12x-x^2) from both sides
0=x^2-12x+15
use quadratic formula which is
x=
where you have
0=ax^2+bx+c
so
a=1
b=-12
c=15
subsitute
x=
x=
x=
x=
x=6+/-
x=6+
or 6- 
or aprox
x=10.5826 or 1.41742
the numbers are 10.5826 and 1.41742
x+y=12
solve
x+y=12
subtract x from both sides
y=12-x
subsitute
xy=15
x(12-x)=15
distribute
12x-x^2=15
subtract (12x-x^2) from both sides
0=x^2-12x+15
use quadratic formula which is
x=
where you have
0=ax^2+bx+c
so
a=1
b=-12
c=15
subsitute
x=
x=
x=
x=
x=6+/-
x=6+
x=10.5826 or 1.41742
the numbers are 10.5826 and 1.41742