What times what equals 108 but added equals 18

One way is to expand theh 18
and multily them
1*17=17, nope
2*16=32, nope
3*15=45, nope
4*14=56, nope
5*13=65, nope
6*12=72, nope
7*11=77, nope
8*10=80, nope
9*9=81, nope

so we aren't going to get it that way

xy=108
x+y=18
solve for 1
minus x both sides in 2nd equation
y=18-x
sub 18-x for y in other equaiton
x(18-x)=108
18x-x²=108
times -1 both sides
x²-18x=-108
add 108 both sides
x²-18x+108=0
we know we can't factor so we has to use quadratic formula

for
ax²+bx+c=0
x=

given
1x²-18x+108
a=1
b=-18
c=108
rememeber that √-1=i

x=
x=
x=
x=
x=


the numbers are 9+3i√3 and 9-3i√3

Whose mistake? can you give more details to what the question is asking?