xy=-126
x+y=6
minus x
y=6-x
sub
x(6-x)=-126
6x-x^2=-126
minus (6x-x^2) both sides
0=x^2-6x-126
in form
ax^2+bx+c=0
x=\(\frac{ -b+/-\sqrt{b^{2}-4ac} }{2a}\)
a=1
b=-6
c=-126
x=\(\frac{ -(-6)+/-\sqrt{(-6)^{2}-4(1)(-126)} }{2(1)}\)
x=\(\frac{ 6+/-\sqrt{36+504} }{2}\)
x=\(\frac{ 6+/-\sqrt{540} }{2}\)
x=\(\frac{ 6+/-6\sqrt{150} }{2}\)
x=\(3+/-3\sqrt{150}\)
the numbers are
\(3+3\sqrt{150}\) and \(3-3\sqrt{150}\)
